Two's Complement (Cambridge (CIE) IGCSE Computer Science): Revision Note
Exam code: 0478 & 0984
Two's Complement
What is two's complement?
Examiner Tips and Tricks
Cambridge IGCSE 0478 requires you to represent signed binary values using 8-bit two’s complement only. This page follows the exact bit structure and method examiners expect to see.
In IGCSE Computer Science, two's complement is a method of using signed binary values to represent negative numbers
Using two's complement the left most bit is designated the most significant bit (MSB)
In two’s complement, if the MSB is 1, it represents a negative number
In 8-bit, the MSB column has a weight of -128, while the remaining columns keep their positive values
-128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |
|---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | = -1 |
In the example above, to find the value, add together the column values where there is a 1
Here, all columns are 1, so the sum is -128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = -1
The two's complement representation of -1 is 11111111
Quick two's complement conversion
To represent -76
Write out the positive version of the number
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | |
|---|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | = 76 |
Starting from the least significant bit (right most column), copy out the binary values up to and including the first 1
-128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 0 | 0 |
For the remaining digits, invert them (0s to 1s/1s to 0s)
-128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
-128 + 32 + 16 + 4 = -76
The two's complement representation of -76 is 10110100
Examiner Tips and Tricks
The “flip and add 1” trick isn’t shown here, but the method above is what examiners prefer: copy from the right, then invert. It’s reliable, repeatable, and rewarded in papers.
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