Teaching Computing at KS3Session 2

Sue Sentance and Sophie BakerSue.sentance@anglia.ac.uk

From the CAS curriculumKEY STAGE 2

Introduction to binary representation [representing names, objects or ideas as sequences of 0s and 1s].

KEY STAGE 3Introduction to binary manipulation. Representations of unsigned integers

Today’s session5:00 – 6:00 Binary numbers – converting

between denary and binary 6.00 – 7.00 Programming in Scratch

Storing Binary Numbers

Inside the computer each binary digit is stored in a unit called a bit.

A series of 8 bits is called a byte.

A bit can take the values 0 and 1

What is meant by?1 byte ? 1 nibble ?

1 kilobyte ?1 megabyte ?1 gigabyte ?1 terabyte ?

Storing data1 byte = 8 bits1 nibble = 4 bits

1 kilobyte = 1024 bytes = 2 10 bytes

1 megabyte = 2 20 bytes = 210 kilobytes1 gigabyte = 2 30 bytes = 210 megabytes1 terabyte = 2 40 bytes = 2 10 gigabytes

1 byte 1 nibble

1 kilobyte 1 megabyte 1 gigabyte 1 terabyte

Learning binary numbersConverting binary to denaryConverting denary to binary

Number BasesBase 10 (Denary)10 different symbols to

represent values:0 1 2 3 4 5 6 7 8 9

Values greater than 9 are represented using the place value convention:100s 10s 1s 3 5 7= 3x100 + 5x10 + 7x1ie. Three hundred and fifty seven

Base 2 (Binary)2 different symbols to

represent values:0 1

Values greater than 1 are represented using the place value convention:8s 4s 2s 1s 1 1 0 1

= 1x8 + 1x4 + 0x2 + 1x1=Thirteen10 1100

7 5 3

12481011

Binary numbers

0

Binary numbers

1

ActivityBinary counting exercise

How to convert Binary Numbers to denary

8+ 0+ 2 + 0 = 10

in Denary

Place values

128 4

11 00

How to convert Binary Numbers to denary

128+0+0+16+8+ 0+ 2 +1 = 155

in Denary

Place values 12128 64 32 16 8 4

0 0 111 100

Converting binary to denary

Convert the binary number 1011 0111 into denary:

Answer128 64 32 16 8 4 2

1 1 0 1 1 0 1 1 1=128+32+16+4+2+1=

183

Conversion ExerciseConvert the following binary numbers into denary:

0 0 1 0 1 0 1 0 0 0 1 0 0 1

1 0 1 1 1 0 1 0 1 0 1 1 1 1

1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1

Conversion ExerciseConvert the following binary numbers into denary:

Answers in red:

0 0 1 0 1 0 1 0 0 0 1 0 0 1

1 0 1 1 1 0 1 0 1 0 1 1 1 1

1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1

1 2 4 9

5 6 10 15

12 21 23 31

Teaching binaryHolding cards up activityFinger binaryCisco binary gameCS Unplugged actitivies

Converting Denary to BinaryWrite down the column headings for the binary number:

64 32 16 8 4 21

Process each column from left to right. If the denary number to be translated is greater than or

equal to the column heading, place a 1 in the column and subtract the value of the column from the denary value.

If the denary value is smaller than the column heading, place a 0 in the column.

ExampleConvert 27:27 < 64, so 0 into 64-column

64 32 16 8 4 210

27 < 32, so 0 into 32-column

0

27 > 16, so 1 into 16-column, new value = 27 – 16 = 11

1

11 > 8, so 1 into 8-column, new value = 11 – 8 = 3

1

3 < 4, so 0 into 4-column

0

3 > 2, so 1 into 2-column, new value = 3 – 2 = 1

1

1 = 1, so 1 into 1-column

1

Storing Numbers - Binary

EXAMPLEConvert the denary number 227 into binary:

128 64 32 16 8 4 21 1 1 1 0 0 0 1 1

Convert to Binary 3 5 8 7

11 16 32 21

14 17 48 255

Convert to Binary 3 5 8 7

11 16 32 21

14 17 48 255

11 101 1000 0111

1011 10000 100000 10101

1110 10001 110000 11111111

Summary – why teach binary?

Binary is a set of instructions used to control the computer, and works with 1s and 0s

The computer understands them as on or off signals.

If the decimal system were used, there would need to be 10 different voltages, in which case there'd be more room for error with resistors etc., and therefore more room for corruption of data.

Today, the elementary building block for all modern computer systems is the transistor. A transistor is simply a switch, much like the light switch mentioned earlier.

A transistor can be in an off state, which does not allow electricity to flow, or in an on state, in which electricity can pass unimpeded. A transistor is a solid-state device that has no mechanical or moving parts. The switching of a transistor from the off state to the on state, or vice versa, is done electronically rather than mechanically. This allows it to be fast as well as extremely small.

So learning binary helps students to understand how a computer works