O-LevelComputer ScienceData Representation2210/11 · May/June 2023 · Q111 Marks

Binary is a number system used by computers.

(a)Tick (✔) one box to show which statement about the binary number system is correct. A It is a base 1 system B It is a base 2 system C It is a base 10 system D It is a base 16 system[1]
(b)Denary numbers are converted to binary numbers to be processed by a computer. Convert these three denary numbers to 8-bit binary numbers. 50 102 221 Working space[3]
(c)Binary numbers are stored in registers. Negative denary numbers can be represented as binary using two's complement. Complete the binary register for the denary number –78 You must show all your working. Working space Register:[2]
(d)Two 8-bit binary numbers are given. Add the two 8-bit binary numbers using binary addition. Give your answer in binary. Show all your working. 00110011 +01100001[3]
(e)Two binary numbers are added by a computer and an overflow error occurs. Explain why the overflow error occurred.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[1] B
[1] One mark per each correct conversion • 00110010 • 01100110 • 11011101
[1] One mark for full method of working e.g. conversion to binary then flipping and adding 1
[1] One mark for correct answer • 10110010
[1] One marks per each correct nibble
[1] One mark for correct working in binary (showing 4 correct carries) 11 11 00110011 01100001 10 0 1 0100
[2] Two from: • The result of the calculation is greater than 255 // The value generated is larger than can be stored in the register • The result of the calculation would require more than 8 bits to be represented // A register has a predetermined number of bits and there are too many bits for it

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