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Computing Academy GCSE Computer Science

Two’s Complement Two's

Two’s Complement Two's complement is a methodology used by computers to represent and process negative integers, and it’s a simple way of performing binary subtraction. To get the two's complement notation of an integer: 1. Write out the number in binary 2. Invert the digits 3. Add one to the result Two’s Complement Example Let’s turn the decimal integer ‘59’ into two’s complement negative notation. 1. First we write out the binary equivalent of 59. 128 64 32 16 8 4 2 1 0 0 1 1 1 0 1 1 2. Next, we invert the digits – so we turn 1s into 0s and 0s into 1s 128 64 32 16 8 4 2 1 1 1 0 0 0 1 0 0 3. Finally, we add one to the result 128 64 32 16 8 4 2 1 1 1 0 0 0 1 0 1 So, 59 is represented as 00111011 in binary and 11000101 in two’s complement notation. 67

Binary Subtraction Now we’re comfortable with two’s complement we can use it to perform binary subtraction. Let’s say we want to subtract 9 from 49. 1. First, we write out these numbers in binary 128 64 32 16 8 4 2 1 0 0 1 1 0 0 0 1 - 0 0 0 0 1 0 0 1 We now convert the number to be subtracted (the 9 or 00001001) into two’s complement. 2. We invert the second number 128 64 32 16 8 4 2 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 3. We then add one to the second number 128 64 32 16 8 4 2 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 68

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