What range of integers can 8-bit two's complement represent?

An 8-bit two's complement number ranges from −128 to +127.

How can you tell whether an 8-bit two's complement number is negative?

A two's complement number is negative when its most significant bit is 1. A number whose MSB is 0 is zero or positive.

Describe how to turn a positive binary number into its negative in two's complement.

Write the positive number in binary and invert every bit. Add 1 to the inverted pattern to give the negative number.

Convert −45 to 8-bit two's complement.

The value −45 is 11010011 in 8-bit two's complement. Positive 45 is 00101101, its inverse is 11010010, and adding 1 gives 11010011.

Edexcel GCSE Computer Science 1CP2

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Two's complement

3 things to know
Paper 1

Overview

Two's complement representation, the range −128 to +127, recognising negative values, worked conversions in both directions, and why the CPU uses it.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What range does 8-bit two's complement cover, how is a negative value recognised, and how is one made?

Key term

What is two's complement?

Key term

What is the place value of the most significant bit in 8-bit two's complement?

Questions from this subtopic

Each one with the model answer underneath.

1
What is two's complement?
Model answer
Two's complement is a method of representing signed integers, positive and negative, in binary. The most significant bit carries a negative place value.
2
What is the place value of the most significant bit in 8-bit two's complement?
Model answer
The most significant bit is worth −128 in 8-bit two's complement. The other seven bits keep their usual values from 64 down to 1.
3
What range of integers can 8-bit two's complement represent?
Model answer
An 8-bit two's complement number ranges from −128 to +127.
4
How can you tell whether an 8-bit two's complement number is negative?
Model answer
A two's complement number is negative when its most significant bit is 1. A number whose MSB is 0 is zero or positive.
5
Describe how to turn a positive binary number into its negative in two's complement.
Model answer
Write the positive number in binary and invert every bit. Add 1 to the inverted pattern to give the negative number.
6
Convert −45 to 8-bit two's complement.
Model answer
The value −45 is 11010011 in 8-bit two's complement. Positive 45 is 00101101, its inverse is 11010010, and adding 1 gives 11010011.

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