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Two's complement signed integers
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Unsigned binary can only store positive numbers. Two's complement lets 8 bits store negative numbers too.
Unsigned and signed
An unsigned 8-bit integer stores 0 to 255.
In two's complement, the most significant (left) bit is worth -128 instead of +128.
So 8 bits store -128 to +127. If the left bit is 1, the number is negative.
In two's complement, the most significant (left) bit is worth -128 instead of +128.
So 8 bits store -128 to +127. If the left bit is 1, the number is negative.
Making a negative number
To store -5:
1. Write +5 in binary: 00000101
2. Flip every bit: 11111010
3. Add 1: 11111011
1. Write +5 in binary: 00000101
2. Flip every bit: 11111010
3. Add 1: 11111011
Reading a negative number
Add the place values, remembering the left bit is -128.
10000001 = -128 + 1 = -127
Positive numbers look the same as unsigned: 01000001 = 65.
10000001 = -128 + 1 = -127
Positive numbers look the same as unsigned: 01000001 = 65.
Convert -20 to 8-bit two's complement.
- +20 = 00010100
- Flip: 11101011
- Add 1: 11101100
Answer: 11101100
In 8-bit two's complement the left bit is worth -128, giving a range of -128 to +127. To make a negative: write the positive, flip the bits, add 1.
The interactive lesson includes the diagrams for this topic.
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