Binary addition, overflow and shifts – GCSE Computer Science exam questions with mark scheme

1Grade 6–74 marks

(a) Add together the following two 8-bit binary numbers. Show your working. [2]

  01101101
+ 01011011

(b) A student adds 11010110 and 01100011 using an 8-bit register. The register stores the result 00111001.

Explain why the stored result is incorrect. [2]

(a) Carries shown correctly / at least four bits correct from the right (…1000)(1)
(a) 11001000 fully correct(1)
(b) An overflow (error) has occurred(1)
(b) The correct answer (313 / 100111001) needs 9 bits / is greater than 255, so the 9th bit / final carry is lost / cannot be stored in an 8-bit register(1)
Answer: (a) 11001000 (b) Overflow: result 313 needs 9 bits, so the carry out of the 8th bit is lost
Examiner tip: Always show your carries – if the final answer has one slip you can still get the working mark.

2Grade 6–74 marks

(a) Perform a 2-place left binary shift on 00010110. [1]

(b) State the effect this shift has on the denary value of the number. [1]

Explain why the result is not exactly 107 ÷ 4. [2]

(a) 01011000(1)
(b) Multiplies it by 4; allow 22 → 88(1)
(c) The two right-most bits (1 and 1) are shifted off the end / lost(1)
(c) So precision is lost: 107 ÷ 4 = 26.75 but the remainder / fractional part (0.75) cannot be stored, so the result is 26(1)
Answer: (a) 01011000 (b) ×4 (c) The bits 11 are lost off the right-hand end, so the 0.75 is lost (26 not 26.75)
Examiner tip: A left shift of n places multiplies by 2ⁿ – say 'multiplies by 4', not just 'makes it bigger'.

Book a free introductory session and we'll find exactly which step is costing you.