Addition and subtraction of binary integers

Addition and subtraction of binary integers.

1.4.1 Data Types

Data Types — Note 4 of 10

Candidates should be able to perform addition and subtraction on integer binary numbers. (These numbers could be positive or negative using two’s complement representation.)

What you need to know

Binary addition follows simple rules with carries. Subtraction is carried out by adding the two's complement of the number being subtracted, so a computer only needs circuitry for addition.

What to know

Addition rules: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).
Work from the right (least significant bit) to the left, carrying as you go.
Subtraction: to calculate A - B, convert B to its two's complement negative and ADD it to A. Ignore any carry out of the MSB.
In two's complement, overflow has occurred if two positive numbers give a negative result, or two negative numbers give a positive result.

Key terms

Overflow: The result of a calculation is too large to fit in the number of bits available, so the result is wrong.

Exam technique

Tip:Show your carries clearly; method marks are often available even if the final answer is wrong.
Mistake:Treating a carry out of the MSB as an error in two's complement subtraction. That carry is simply discarded.

Code examples

Subtraction: 45 - 20 by adding -20

text

  45     0 0 1 0 1 1 0 1
+ -20    1 1 1 0 1 1 0 0
        ---------------
       1 0 0 0 1 1 0 0 1   -> discard the carry out of the MSB
Result   0 0 0 1 1 0 0 1   = 25