math1003 1.8 - converting from binary and hex to decimal

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MATH1003 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001 1.8 Converting from Binary and Hexadecimal to Decimal

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Page 1: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

1.8Converting from Binary and Hexadecimal to Decimal

Page 2: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Goal

To correctly convert binary and hexadecimal numbersto their equivalent decimal numbers

Page 3: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Page 4: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

11010012

Page 5: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

Page 6: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

Page 7: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 8: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 9: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 10: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 11: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 12: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 13: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 14: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

The place values of the binary number system are powers of 2.

Page 15: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 20

11010012

Page 16: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

Page 17: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

2

Page 18: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

24

Page 19: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248

Page 20: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

24816

Page 21: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

2481632

Page 22: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

Page 23: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

You’ll notice that the place values double as we go from right to left.

248163264

Page 24: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

You’ll notice that the place values double as we go from right to left.

248163264

Page 25: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

Page 26: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 27: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 28: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 29: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 24 23 22 21 201

11010012

248163264

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 30: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 23 201

11010012

83264

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 31: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 23 201

11010012

83264

11010012

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 32: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 23 201

11010012

83264

11010012

= 64 + 32 + 8 + 1

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 33: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 1 0 0 1

Place value 26 25 23 201

11010012

83264

11010012

= 64 + 32 + 8 + 1= 105

To calculate the decimal equivalent, add the place values wherethere is a “1”.

Page 34: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Page 35: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

1100.1012

Page 36: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

1100.1012

In this example, we have a binary number that has a “point” (ithas a fractional part).

Page 37: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20

1100.1012

In this example, we have a binary number that has a “point” (ithas a fractional part).

.

Page 38: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20 2-1 2-2 2-3

1100.1012

.

Page 39: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20 2-1 2-2 2-3

1100.1012

Place values to the right of the “point” have negative exponents.

.

Page 40: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20 2-1 2-2 2-3

1100.1012

.

Page 41: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20 2-1 2-2 2-3

1100.1012

.

Let’s fill in the place values with their decimal values.

Page 42: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 23 22 21 20 2-1 2-2 2-3

1100.1012

.1248

Let’s fill in the place values with their decimal values.

Page 43: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 2-1 2-2 2-3

1100.1012

.Remember that 2-1

is the same as 121

Page 44: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 121 2-2 2-3

1100.1012

.

Page 45: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12 2-2 2-3

1100.1012

.

Page 46: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

122 2-3

1100.1012

.

Page 47: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14 2-3

1100.1012

.

Page 48: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

123

1100.1012

.

Page 49: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.

Page 50: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

Note that the denominators have the same pattern as the placevalues to the left of the “point” (except in the reverse direction).

.

Page 51: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

Note that the denominators have the same pattern as the placevalues to the left of the “point” (except in the reverse direction).

.

Page 52: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.

Page 53: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.

Let’s fill in the place values with their decimal values.

Page 54: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5

Let’s fill in the place values with their decimal values.

Page 55: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25

Let’s fill in the place values with their decimal values.

Page 56: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Let’s fill in the place values with their decimal values.

Page 57: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Page 58: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

Page 59: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

Page 60: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

Page 61: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

X X X

Page 62: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

X X X

1100.1012

Page 63: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

X X X

1100.1012

= 8 + 4 + 0.5 + 0.125

Page 64: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 1 0 0 1 0 1

Place value 8 4 2 1 12

14

18

1100.1012

.0.5 0.25 0.125

Similar to our last example, to calculate the decimal equivalent, add the place values where there is a “1”.

X X X

1100.1012

= 8 + 4 + 0.5 + 0.125= 12.625

Page 65: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 66: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 67: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 68: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 69: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 70: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 71: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.

Page 72: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625

Page 73: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625

Page 74: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625X

Page 75: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625X

Page 76: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625X X

Page 77: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625

101.11012

X X

Page 78: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625

101.11012

= 4 + 1 + 0.5 + 0.25 + 0.0625

X X

Page 79: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary to Decimal Conversion

Digit 1 0 1 1 1 0 1

Place value 4 2 1 0.5 0.25 0.125

101.11012

.0.0625

101.11012

= 4 + 1 + 0.5 + 0.25 + 0.0625= 5.8125

X X

Page 80: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Page 81: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

3B4.616

Page 82: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 83: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 84: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 85: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 86: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 87: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.160161162

Page 88: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.161162

Page 89: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.161162

Page 90: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.162

Page 91: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.162

Page 92: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.

Page 93: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.062516-1

3B4.616

.

Page 94: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

Page 95: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

Page 96: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

Page 97: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

= 3 • 256 + B • 16 + 4 • 1 + 6 • 0.0625

Page 98: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

= 3 • 256 + B • 16 + 4 • 1 + 6 • 0.0625

Page 99: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

= 3 • 256 + B • 16 + 4 • 1 + 6 • 0.0625= 3 • 256 + 11 • 16 + 4 • 1 + 6 • 0.0625

Page 100: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

= 3 • 256 + B • 16 + 4 • 1 + 6 • 0.0625= 3 • 256 + 11 • 16 + 4 • 1 + 6 • 0.0625= 768 + 176 + 4 + 0.375

Page 101: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 3 B 4 6

Place value 256 16 1 0.0625

3B4.616

.

3B4.616

= 3 • 256 + B • 16 + 4 • 1 + 6 • 0.0625= 3 • 256 + 11 • 16 + 4 • 1 + 6 • 0.0625= 768 + 176 + 4 + 0.375= 948.375

Page 102: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

Page 103: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

Page 104: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

54.D216

Page 105: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

54.D216

= 5 • 161 + 4 • 160 + D • 16-1 + 2 • 16-2

Page 106: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

54.D216

= 5 • 161 + 4 • 160 + D • 16-1 + 2 • 16-2

= 5 • 161 + 4 • 160 + 13 • 16-1 + 2 • 16-2

Page 107: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

54.D216

= 5 • 161 + 4 • 160 + D • 16-1 + 2 • 16-2

= 5 • 161 + 4 • 160 + 13 • 16-1 + 2 • 16-2

= 80 + 4 + 0.8125 + 0.0078125

Page 108: Math1003 1.8 - Converting from Binary and Hex to Decimal

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Hexadecimal to Decimal Conversion

Digit 5 4 D 2

Place value 161 160 16-1 16-2

54.D216

.

54.D216

= 5 • 161 + 4 • 160 + D • 16-1 + 2 • 16-2

= 5 • 161 + 4 • 160 + 13 • 16-1 + 2 • 16-2

= 80 + 4 + 0.8125 + 0.0078125= 84.8203125