Edexcel 1CP2 · Topic 2 · 2.1c

Two's
Complement

Representing Negative Numbers · Sign Bit · Conversion Method

CSZoneEdexcel GCSE Computer Science 1CP2

Why Two's Complement?

Representing Negative Numbers in Binary

Computers need to represent negative numbers. Two's complement is the standard method. The most significant bit (MSB) — the leftmost bit — acts as the sign bit: 0 = positive, 1 = negative.

In 8-bit two's complement, the MSB column has value -128 (not +128)

Range of 8-bit two's complement: -128 to +127

If MSB = 1, the number is negative; if MSB = 0, it is positive

Finding Two's Complement

Method: Invert All Bits, Then Add 1

Convert -45 to 8-bit two's complement:

Step 1: write +45 in binary: 00101101
Step 2: invert all bits: 11010010
Step 3: add 1: 11010010
+ 1
Result: 11010011

Verify: -128 + 64 + 16 + 2 + 1 = -45 ✓

Reading a Negative Two's Complement Number

Example: What is 11001010?

11001010 — MSB is 1, so it's NEGATIVE

Column values: -128, 64, 32, 16, 8, 4, 2, 1
Bits: 1 1 0 0 1 0 1 0

-128 + 64 + 8 + 2 = -54

Exam tip:The MSB is worth -128 (not +128). All other bits keep their normal positive values.

Exam Practice

Have a go at this question

Edexcel-style question

Using 8-bit two's complement, find the binary representation of -12. Show your working.

3 marks

+12 = 00001100 [1]
Invert: 11110011 [1]
Add 1: 11110100 [1] = -12 in two's complement

Key Takeaways

What to Remember

Two's complement: MSB = sign bit (0=positive, 1=negative)

8-bit range: -128 to +127; MSB column value = -128

To negate: invert all bits → add 1

To read negative two's complement: use -128 for MSB, normal values for rest