Units of information & binary arithmetic (addition, shifts) – GCSE Computer Science exam questions with mark scheme

1Grade 4–54 marks

(a) Add together the following three 8-bit binary numbers. Give your answer in binary and show your working. [2]

  00110101
  01001011
+ 00010110

(b) Convert the three numbers and your answer to (a) into denary to check that your answer is correct. [2]

(a) Evidence of correct carries / working; or final answer with no more than one bit wrong. A fully correct answer 10010110 scores both marks even if working is not shown(1)
(a) 10010110 fully correct(1)
(b) The three numbers converted correctly: 53, 75 and 22(1)
(b) Answer converted to 150 and shown to equal 53 + 75 + 22; follow through from their (a) answer converted correctly(1)
Answer: (a) 10010110 (b) 53 + 75 + 22 = 150 and 10010110 = 150
Examiner tip: With three numbers a column can total 3 (binary 11): write 1 and carry 1 into the next column, then remember to add that carry in.

2Grade 6–74 marks

(a) The binary number 00010110 is shifted two places to the left. Give the result as an 8-bit binary number and state the effect of the shift on the value. [2]

(b) A programmer wants to divide the binary number 10110000 by 8 using a binary shift. Describe the shift needed and give the result as an 8-bit binary number. [2]

(a) 01011000(1)
(a) The value is multiplied by 4; allow 22 becomes 88(1)
(b) Shift (logical) right by three places; accept 'shift right 3'(1)
(b) 00010110; accept 10110 (denary 22); follow through from a stated right shift of a different number of places(1)
Answer: (a) 01011000; the value is multiplied by 4 (22 → 88) (b) shift right 3 places; 00010110 (176 ÷ 8 = 22)
Examiner tip: Each place shifted multiplies or divides by 2, so 8 = 2³ means three places – and dividing means shifting right.

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