Number bases & converting between them – GCSE Computer Science exam questions with mark scheme

1Grade 1–33 marks

(a) Convert the binary number 10110110 into denary. [1]

(b) Convert the denary number 45 into binary. [1]

(a) 182(1)
(b) 101101; accept with leading zeros, e.g. 00101101(1)
(c) 16(1)
Answer: (a) 182 (b) 00101101 (c) 16
Examiner tip: Check a conversion by adding the place values back up: 32 + 8 + 4 + 1 = 45.

2Grade 4–54 marks

(a) Convert the hexadecimal number A7 into denary. You must show your working. [2]

(b) Convert the binary number 11011001 into hexadecimal. [2]

(a) Working: A = 10 so 10 × 16 (= 160) + 7; allow 1010 0111 shown as binary(1)
(a) 167(1)
(b) First hex digit D (from 1101)(1)
(b) Second hex digit 9 (from 1001)(1)
Answer: (a) 167 (b) D9
Examiner tip: Split binary into nibbles from the right before converting – each nibble is one hex digit.

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