Two's Complement and Fixed-Point Binary

This lesson covers how computers represent signed integers using two's complement and how fixed-point binary is used to represent fractional numbers. Both are required for the OCR H446 specification.

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Why Signed Numbers?

Computers need to represent both positive and negative integers. Since binary only has 0s and 1s, a convention is needed to distinguish between positive and negative values.

Approaches to Signed Representation

Method	Description	Used in Practice?
Sign and magnitude	The MSB is the sign (0 = positive, 1 = negative); remaining bits = magnitude	Rarely — has +0 and -0
One's complement	Negative = flip all bits of the positive value	Rarely — has +0 and -0
Two's complement	Negative = flip all bits and add 1	Yes — standard method

Two's complement is the standard because:

• There is only one representation of zero
• Addition and subtraction work using the same hardware circuit
• The range is slightly asymmetric but well-defined

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Two's Complement Representation