Two's Complement (Cambridge International IGCSE Computer Science)

Spec point — 1.1.6 · "6 Use two’s complement to represent positive and negative 8-bit binary integers"

Two's Complement

What is two's complement?

Exam Hint 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

• 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

• Starting from the least significant bit(right most column), copy out the binary values up to and including the first 1

• For the remaining digits,invert them (0s to 1s/1s to 0s)

• -128 + 32 + 16 + 4 = -76
• The two's complement representation of -76 is 10110100

Exam Hint 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.