Converting Between Decimal & Binary (AQA GCSE Computer Science)
Revision Note
Written by: James Woodhouse
Reviewed by: Lucy Kirkham
Decimal to Binary Conversion
Decimal to binary conversion
It is important to know the process of converting from decimal to binary to understand how computers interpret and process data
Example 1
To convert the decimal number 45 to binary, start by writing out the binary headings from right to left
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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Start at the leftmost empty column heading (128). Is the decimal number > column heading? (45 > 128) No, put a 0 in the 128 column. Repeat until you put a 1 under a heading. In this example it would be 32
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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0 | 0 | 1 |
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Next subtract column heading from decimal value, 45-32 = 13
Repeat previous two steps until you have a value under each column heading
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
32 + 8 + 4 + 1 = 45
Decimal 45 is 00101101 in Binary
Examiner Tips and Tricks
Don't forget to show your working! Data conversion questions will often be worth 2 marks, 1 for the answer and 1 for your working
Example 2
To convert the decimal number 213 to binary, start by writing out the binary headings from right to left
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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Start at the leftmost empty column heading (128). Is decimal number > column heading? (213 > 128) Yes, put a 1 under the heading.
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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1 |
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Next subtract column heading from decimal value, 213-128 = 85
Repeat process until you have a value under each column heading
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
128 + 64 + 16 + 4 + 1 = 213
Decimal 213 is 11010101 in Binary
Examiner Tips and Tricks
At GCSE you will only be asked to convert from/to binary up to and including 8 binary digits (8 bits). That means you are working with a decimal range of 0-255 (00000000-11111111)
Binary to Decimal Conversion
Example 1
To convert the binary number 1011 to decimal, start by writing out the binary headings from right to left
8 | 4 | 2 | 1 |
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Write in the binary digits under the headings from left to right
8 | 4 | 2 | 1 |
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1 | 0 | 1 | 1 |
Add together any value with a 1 under it
(1 x 8) + (1 x 2) + (1 x 1) = 11
Binary 1011 is 11 in Decimal
Examiner Tips and Tricks
If you are converting from binary to decimal and the binary number ends in 1, the decimal answer must be an odd number!
Example 2
To convert the binary number 01100011 to decimal, start by writing out the binary headings from right to left
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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Write in the binary digits under the headings from left to right
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
Add together any value with a 1 under it
(1 x 64) + (1 x 32) + (1 x 2) + (1 x 1) = 99
Binary 01100011 is 99 in Decimal
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