IGCSE · Practice questions · Binary addition and overflow

Mind the carry.

Six original Cambridge-style questions on binary addition and overflow, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Right to left.

Rules: 1 + 1 = 0 carry 1; 1 + 1 + 1 = 1 carry 1.
Show carries: write each carry above the next column on the left.
Overflow: the result is bigger than the register can hold (more than 255 for 8 bits).
Check: convert the two numbers and the answer to denary.

Calculate

[2 marks]

Add the 8-bit binary integers 00110101 and 01001110. Show your working.

Carries shown correctly (columns 3 to 7 from the right each receive a carry). ✓
Answer 10000011 (53 + 78 = 131). ✓

Explain

[2 marks]

Explain what is meant by an overflow error in binary addition.

A register or device has a predefined limit on the values it can store, e.g. 255 for 8 bits. ✓
Overflow occurs when the result of a calculation is outside this limit, so it needs more bits than are available. ✓

Calculate

[3 marks]

Add 11010110 and 01011100 in an 8-bit register. Give the 8-bit result and state what has happened.

Working with carries gives 1 0011 0010. ✓
The 8-bit register stores 00110010. ✓
Overflow: 214 + 92 = 306, which is more than 255, so the ninth bit is lost (the stored value 50 is wrong). ✓

Recall

[2 marks]

State the largest denary value that can be stored in (a) an 8-bit register and (b) a 16-bit register.

(a) 255. ✓
(b) 65 535. ✓

Apply

[3 marks]

A game stores a player's score in an 8-bit register. The score is 250 and the player earns 10 more points. Explain what happens to the stored score.

250 + 10 = 260, which is more than 255. ✓
260 = 1 0000 0100 needs 9 bits, so an overflow error occurs. ✓
The register keeps only 00000100, so the score shows as 4. ✓

Analysis

[2 marks]

A student adds 01101001 and 00010111 and writes 01111110. Identify the mistake and give the correct answer.

The student wrote 0 for 1 + 1 but did not carry the 1 into the next column. ✓
Correct answer 10000000 (105 + 23 = 128). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.