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Teaching Computing at KS3 Session 2. Sue Sentance and Sophie Baker Sue.sentance@anglia.ac.uk. From the CAS curriculum. KEY STAGE 2 Introduction to binary representation [representing names, objects or ideas as sequences of 0s and 1s].

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teaching computing at ks3 session 2

Teaching Computing at KS3Session 2

Sue Sentance and Sophie Baker

Sue.sentance@anglia.ac.uk

from the cas curriculum
From the CAS curriculum
  • KEY STAGE 2

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

  • KEY STAGE 3Introduction to binary manipulation. Representations ofunsigned integers
today s session
Today’s session

5:00 – 6:00 Binary numbers – converting between denary and binary

6.00 – 7.00 Programming in Scratch

storing binary numbers
Storing Binary Numbers

Inside the computer eachbinarydigit 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
What is meant by?

1 byte ?

1 nibble ?

1 kilobyte ?

1 megabyte ?

1 gigabyte ?

1 terabyte ?

storing data
Storing data

1 byte

1 nibble

1 kilobyte

1 megabyte

1 gigabyte

1 terabyte

1 byte = 8 bits

1 nibble = 4 bits

1 kilobyte = 1024 bytes = 2 10 bytes

1 megabyte = 2 20 bytes = 210 kilobytes

1 gigabyte = 2 30 bytes = 210megabytes

1 terabyte = 2 40bytes = 2 10 gigabytes

learning binary numbers
Learning binary numbers

Converting binary to denary

Converting denary to binary

number bases
Base 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=Thirteen

Number Bases

1

2

100

8

10

1

4

0

1

1

1

3

5

7

how to convert binary numbers to denary
How to convert Binary Numbers to denary

Place values

8+ 0+ 2 + 0 = 10

in Denary

8

4

2

1

1

0

1

0

how to convert binary numbers to denary1
How to convert Binary Numbers to denary

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

in Denary

Place values

128

64

32

16

8

4

2

1

0

0

0

1

1

0

1

1

converting binary to denary
Converting binary to denary

Convert the binary number 1011 0111 into denary:

Answer

128 64 32 16 8 4 2 1 1 0 1 1 0 1 1 1

=128+32+16+4+2+1=183

conversion exercise
Conversion Exercise

Convert 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 exercise1
Conversion Exercise

Convert 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

9

4

15

6

10

5

12

31

23

21

teaching binary
Teaching binary

Holding cards up activity

Finger binary

Cisco binary game

CS Unplugged actitivies

converting denary to binary
Converting Denary to Binary
  • Write down the column headings for the binary number:64 32 16 8 4 2 1
  • 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.
example
Example

Convert 27:

27 < 64, so 0 into 64-column

27 < 32, so 0 into 32-column

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

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

3 < 4, so 0 into 4-column

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

1 = 1, so 1 into 1-column

64 32 16 8 4 2 1

0

0

1

1

0

1

1

storing numbers binary
Storing Numbers - Binary

EXAMPLE

Convert the denary number 227 into binary:

128 64 32 16 8 4 2 1

11 1 0 0 011

convert to binary
Convert to Binary

3 5 8 7

11 16 32 21

14 17 48 255

convert to binary1
Convert to Binary

3 5 8 7

11 16 32 21

14 17 48 255

0111

11

101

1000

10000

100000

10101

1011

110000

11111111

10001

1110

summary why teach binary
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