binary numbers

HASAN FAROOQ HASAN FAROOQ

BB113994BB113994

IMRAN MALIKIMRAN MALIK

BB121014BB121014

INTRODUTIONINTRODUTION

  represents numeric represents numeric values using two values using two symbols: symbols: 

0 & 1 0 & 1

Binary systemBinary system

• But the question will arises in your But the question will arises in your mind that why do computer only use mind that why do computer only use 0, 10, 1

• Answer is simple electronic circuit Answer is simple electronic circuit that only have 2 states (on or off).that only have 2 states (on or off).

• Examples, we have light in a room Examples, we have light in a room for that we have two option , either for that we have two option , either (off or on)(off or on)

RULES FOR ADDITIONRULES FOR ADDITION

0+0 = 0 0 plus 0 equals 0

0+1 = 1 0 plus 1 equals 1

1+0 = 1 1 plus 0 equals 1

1+1 = 10 1 plus 1 equals 10

RULES FOR RULES FOR SUBTRACTIONSUBTRACTION0 – 0 = 00 – 0 = 0

1 – 0 = 11 – 0 = 1

1 – 1 = 01 – 1 = 0

10 – 1 = 110 – 1 = 1

EXAMPLEEXAMPLE

1010110101

0111001110

Binary numbersBinary numbers

1.1. binary describe a binary describe a system that has system that has two digits(0,1)two digits(0,1)

2.2. Decimal system Decimal system has 10 digits(0.9)has 10 digits(0.9)

3.3. We all have 10 We all have 10 fingers and 10 fingers and 10 toes which we toes which we use for addition use for addition and subtraction.and subtraction.

4.4. In binary we In binary we keep things keep things simple and only simple and only use (0,1) just use (0,1) just like computerlike computer

IMRAN IMRAN

CONTINUECONTINUE

FURTHER………… FURTHER…………

Binary systemBinary system

• a transistor with five volts would be a transistor with five volts would be considered "on", while a transistor considered "on", while a transistor with no voltage would be considered with no voltage would be considered "off.“"off.“

• As the binary numbers composed of As the binary numbers composed of only 2 numbers(0,1) you will know only 2 numbers(0,1) you will know how is it possible beyond 2 .how is it possible beyond 2 .

Binary systemBinary system

Binary multiplicationBinary multiplication

    is actually much simpler than is actually much simpler than decimal multiplication. In the case of decimal multiplication. In the case of decimal multiplication, we need to decimal multiplication, we need to remember 3 x 9 = 27, 7 x 8 = 56, remember 3 x 9 = 27, 7 x 8 = 56, and so on. In binary multiplication, and so on. In binary multiplication, we only need to remember the we only need to remember the following, following,

multiplicationmultiplication

• 0 x 0 = 0 0 x 0 = 0 0 x 1 = 00 x 1 = 01 x 0 = 01 x 0 = 01 x 1 = 1 1 x 1 = 1

•     101101   x11 x11  101 (multiplication)  101 (multiplication)101010101111 1111

Binary divisionBinary division

•     100 / 10 =10100 / 10 =10

• 111 / 11 =10111 / 11 =10

• 1010 / 100 =101010 / 100 =10

• 1101 / 11 =1001101 / 11 =100

• 10111 / 10=1011     10111 / 10=1011