Two's complement: negative numbers
Watch the whole lecture free
Make a free account to watch every lecture to the end: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
That was the teaching part. The rest of this lecture is free with an account: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Below zero
- One clever change
- The sign bit
- Positive numbers
- Reading a negative number
Read the transcript of the teaching part
Last time
Before we start: last time, in Logical binary shifts, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Below zero
A freezer at minus eighteen degrees, a bank balance below zero, a game character losing points. Computers need negative numbers too. But a register only holds ones and zeros: there is no minus sign. The answer Cambridge wants is called two's complement.
One clever change
Two's complement makes one clever change. In ordinary binary, the left column is worth one hundred and twenty-eight. In two's complement, it is worth minus one hundred and twenty-eight. Every other column stays the same.
The sign bit
So the left bit tells you the sign. A zero there means the number is positive, and a one there means the number is negative, because minus one hundred and twenty-eight is included.
Positive numbers
Positive numbers look exactly the same as before. October November 2023, Paper 13 asked for one hundred and twenty-three in two's complement. One hundred and twenty-three is 01111011. It starts with zero, so it is positive, and that is the answer.
Reading a negative number
To read a negative number, just add the place values, counting the left column as minus one hundred and twenty-eight. May June 2025, Paper 13: 11001001. Minus one hundred and twenty-eight, plus sixty-four, plus eight, plus one. That is minus fifty-five.
How often it comes up
The whole chapter: Number Systems.
Chapter 1.5: Two's complement
- Two's complement: negative numbers 6 min
Also for IGCSE Computer Science 0478
Which topics come up most in IGCSE Computer Science 0478 past papers, counted from every paper since 2004: Paper 1 topic frequency, Paper 2 topic frequency.