Two's complement Cambridge IGCSE Computer Science revision
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In plain words
Ordinary binary can only count upwards from zero. Two's complement is the usual way to store negative whole numbers as well.
The trick is simple: the leftmost bit is given a negative place value. In 8 bits it is worth −128, not +128. Everything else stays the same.
6 things to know
- The place values of an 8-bit two's complement number are −128, 64, 32, 16, 8, 4, 2, 1.
- If the leftmost bit is 1 the number is negative. If it is 0 the number is positive.
- The range of an 8-bit two's complement number is −128 to +127.
- To read one: add up the place values under the 1s, remembering that the first is −128.
- To write a negative number: write the positive number in 8-bit binary, flip every bit, then add 1.
- The same steps turn a negative number back into its positive: flip every bit and add 1.
Worked example
Write −35 as an 8-bit two's complement number.
- Write +35 in binary: 00100011.
- Flip every bit: 11011100.
- Add 1: 11011101.
- Check with the place values: −128 + 64 + 16 + 8 + 4 + 1 = −35.
Worked example
What is the denary value of the two's complement number 10110100?
- Place values under the 1s: −128, 32, 16 and 4.
- −128 + 32 + 16 + 4 = −76.
Tips and tricks
- Always check a negative answer with the place values. If the leftmost bit is not 1, something has gone wrong.
- Flip, then add 1. Adding 1 first and then flipping gives the wrong number.
It lands in your notebook with its questions as flashcards.
Two's complement: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
In 8-bit two's complement, what is the place value of the leftmost bit?
It is the same size as in ordinary binary but negative.
What is the 8-bit two's complement number 11111111 in denary?
−128 + 127 = −1.
What range of numbers can 8-bit two's complement store?
The smallest is 10000000 = −128. The largest is 01111111 = 127.
What is −6 in 8-bit two's complement?
+6 is 00000110. Flip to get 11111001, then add 1.
What is the 8-bit two's complement number 10000011 in denary?
−128 + 2 + 1 = −125.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 5 marks. Write your answers on paper, then check them.
Two's complement
Cambridge IGCSE Computer Science 0478 · 5 marks · papermunch.org
Name ______________________________ Date ______________
Write the denary number −20 as an 8-bit two's complement number.[2]
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11101100. (+20 is 00010100. Flipped: 11101011. Add 1.)
Convert the 8-bit two's complement number 11010110 to denary.[2]
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−42. −128 + 64 + 16 + 4 + 2.
State how you can tell from its bits that a two's complement number is negative.[1]
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Its leftmost (most significant) bit is 1.
Answers: Two's complement
- 1. 11101100. (+20 is 00010100. Flipped: 11101011. Add 1.)
- 2. −42. −128 + 64 + 16 + 4 + 2.
- 3. Its leftmost (most significant) bit is 1.