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Practise 26 exam-style questions on Binary addition and overflow for Cambridge IGCSE Computer Science (Paper 1). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Add the 8-bit binary integers 00111111 and 00000001.
Give your answer as an 8-bit binary integer.
00111111 + 00000001 = 01000000 (63 + 1 = 64)
Adding 1 to a run of 1s turns each of them into 0 with a carry, until the carry reaches a 0, which becomes 1. So 00111111 + 1 = 01000000.
01000000
accept with or without spaces
A computer game stores each player's score in an 8-bit register. Players with high scores find that their score suddenly drops to a very small number.
Explain how the programmer could stop this happening.
The score drops because of overflow: the total goes above 255, the largest value 8 bits can hold. The programmer could store the score in a 16-bit register instead, which can hold values up to 65 535, so high scores no longer overflow.
Overflow happens because the register has a fixed limit. Increasing the number of bits raises the limit (16 bits: 65 535), or the program can check the size of the result before storing it.
Store the score using more bits, e.g. a 16-bit register
max 2
A 16-bit register can hold values up to 65 535, so the overflow will not happen for normal scores
Check before adding whether the result will be greater than 255 and stop at the maximum / show a message
Add the positive 8-bit binary integers 01110110 and 00011011.
Give your answer in 8-bit binary and in denary.
01110110
+ 00011011
= 10010001
Denary: 128 + 16 + 1 = 145 (check: 118 + 27 = 145)
Almost every column produces a carry, and in the 16s column 1 + 1 plus a carry gives 1 carry 1. Converting the result to denary and comparing it with the denary sum of the two numbers (118 + 27) is the best way to check the binary working.
First nibble: 1001
binary answer 10010001; one mark for each correct nibble
Second nibble: 0001
Denary: 145
allow follow-through from an incorrect binary answer
Complete the description of overflow. Give the missing terms A to D, using terms from this list.
127, 255, 256, 9th, 16th, correct, incorrect, overflow, syntax
An 8-bit register can store denary values from 0 to A. When two 8-bit numbers are added, a carry out of the most significant bit creates a B bit. The register cannot store this bit, so an C error occurs and the result stored in the register is D.
A: 255
B: 9th
C: overflow
D: incorrect
An 8-bit register holds 0 to 255. A carry out of the 8th bit would need a 9th bit, which the register does not have, so an overflow error occurs and the stored result is wrong.
A: 255
B: 9th
C: overflow
D: incorrect
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