Edexcel 1CP2 · Topic 2 · 2.1d

Binary
Arithmetic

Binary Addition · Overflow · Binary Shifts · Multiplication & Division

CSZoneEdexcel GCSE Computer Science 1CP2

Binary Addition Rules

Adding Binary Numbers

+ 0 = 0     0 + 1 = 1
+ 0 = 1     1 + 1 = 10 (write 0, carry 1)
+ 1 + 1 = 11 (write 1, carry 1)

01101010 (106)
+ 00110101 (53)
──────────────
10011111 (159)

Overflow

When the Result Doesn't Fit

Overflow occurs when the result of a calculation is too large to be stored in the number of available bits. In 8-bit, the maximum positive value is 255 (unsigned) or 127 (signed two's complement). Adding two large numbers can cause overflow — the carry out of the MSB is lost.

11111111 (255)
+ 00000001 (1)
──────────────
1 00000000 ← carry lost! Result appears to be 0 (OVERFLOW)

Binary Shifts

Multiply and Divide by Powers of 2

Left shift: move all bits left by n positions; fill with zeros on right. Equivalent to multiplying by 2ⁿ.

Right shift: move all bits right by n positions; fill with zeros on left. Equivalent to dividing by 2ⁿ (integer division).

00000101 = 5
Left shift 2: 00010100 = 20 (5 × 4)
Right shift 1: 00000010 = 2 (5 ÷ 2, integer)

Exam Practice

Have a go at this question

Edexcel-style question

Add the following 8-bit binary numbers: 01011011 + 00110110. State the result in binary and denary, and identify if overflow has occurred.

3 marks

01011011 (91) + 00110110 (54) = 10010001 [1]
= 128 + 16 + 1 = 145 in denary [1]
No overflow — result fits in 8 bits (MSB = 1, but treating as unsigned 145 < 255) [1]

Key Takeaways

What to Remember

1+1=10 (write 0, carry 1); 1+1+1=11 (write 1, carry 1)

Overflow: result too large for available bits — carry lost from MSB

Left shift n positions = multiply by 2ⁿ

Right shift n positions = divide by 2ⁿ (integer division)