Converting Between Binary & Denary (Cambridge (CIE) IGCSE Computer Science)
Revision Note
Written by: Robert Hampton
Reviewed by: James Woodhouse
Denary to Binary Conversion
How do you convert denary to binary?
It is important to know the process of converting from denary to binary to understand how computers interpret and process data
To convert from denary to binary you must start by writing out a binary number line
Find the first column heading with a value larger than the denary value you are converting
Write down each column heading to the right (not including the largest heading) until you reach 1
32,768 | 16,384 | 8,192 | 4,096 | 2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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Example 1
To convert the denary number 45 to binary, start by writing out the binary number line
The first column heading larger than 45 is 64, so the number line would be:
32 | 16 | 8 | 4 | 2 | 1 |
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Start at the leftmost empty column heading (32)
Divide column heading into denary number (how many times does 32 fit into 45?)
1 time with 13 remaining
13 | |||||
32 | 16 | 8 | 4 | 2 | 1 |
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1 |
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Repeat with next column heading (how many times does 16 fit into 13?)
0 times with 13 remaining
13 | 13 | ||||
32 | 16 | 8 | 4 | 2 | 1 |
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1 | 0 |
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Repeat until all columns have a binary value
13 | 13 | 5 | 1 | 1 | 0 |
32 | 16 | 8 | 4 | 2 | 1 |
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1 | 0 | 1 | 1 | 0 | 1 |
Denary 45 is 101101 in binary (6 bits)
Examiner Tips and Tricks
Always read the question carefully to check for how many bits are expected in your answer
In the example above, a 6 bit answer has been given
If they question requires an 8 bit answer, add 2 extra 0s to the start of the answer
Denary 45 is 101101 in 6 bit binary and 00101101 in 8 bit binary
Example 2
To convert the denary number 3059 to binary, start by writing out the binary number line
The first column heading larger than 3059 is 4096, so the number line would be:
2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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Start at the leftmost empty column heading (2048)
Divide column heading into denary number (how many times does 2048 fit into 3059?)
1 time with 1011 remaining
1011 | |||||||||||
2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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1 |
Repeat with next column heading (how many times does 1024 fit into 1011?)
0 times with 1011 remaining
1011 | 1011 | ||||||||||
2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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1 | 0 |
Repeat until all columns have a binary value
1011 | 1011 | 499 | 243 | 115 | 51 | 19 | 3 | 3 | 3 | 1 | 0 |
2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
Denary 3059 is 101111110011 in binary (12 bits)
Binary to Denary Conversion
To convert from binary to denary, count how many bits make up the value
Write out the column headings for the number of bits given from right to left
Add together any column heading with a value of 1 in the column
Example 1 (4 bits)
To convert the binary number 1011 to denary, 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 column heading with a 1 under it
(1 x 8) + (1 x 2) + (1 x 1) = 11
Binary 1011 is 11 in denary
Examiner Tips and Tricks
If you are converting from binary to denary and the binary number ends in 1, the denary answer must be an odd number!
Example 2 (8 bits)
To convert the binary number 01100011 to denary, 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 column heading with a 1 under it
(1 x 64) + (1 x 32) + (1 x 2) + (1 x 1) = 99
Binary 01100011 is 99 in denary
Example 3 (14 bits)
To convert the binary number 01110001110100 to denary, start by writing out the binary headings from right to left
8,192 | 4,096 | 2,048 | 1,024 | 512 | 256 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
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0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
Add together any column heading with a 1 under it
(1 x 4096) + (1 x 2048) + (1 x 1024) + (1 x 64) + (1 x 32) + (1 x 16) + (1 x 4) = 7284
Binary 01110001110100 is 7284 in denary
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