IGCSE · Practice questions · Logical binary shifts

Double or halve.

Six original Cambridge-style questions on logical binary shifts, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Keep these straight

Lose, then fill.

Move: shift every bit the given number of places.
Lose: bits pushed past the end of the register are lost.
Fill: 0s enter at the opposite end; keep exactly 8 bits.
Effect: left n places × 2ⁿ, right n places ÷ 2ⁿ, correct only if no 1s are lost.

Apply

[2 marks]

Perform a logical left shift of 2 places on 00101011. State the effect on the denary value.

Result 10101100. ✓
The value is multiplied by 4 (43 becomes 172). ✓

Apply

[2 marks]

Perform a logical right shift of 3 places on 11001000. State the effect on the denary value.

Result 00011001. ✓
The value is divided by 8 (200 becomes 25). ✓

Explain

[2 marks]

Describe what happens to the bits in a register during a logical left shift of one place.

Every bit moves one place to the left and the most significant bit is lost. ✓
A 0 is shifted in at the right-hand (least significant) end. ✓

Calculate

[3 marks]

01011010 is shifted right 2 places. (a) Give the result in binary and denary. (b) Explain why the answer is not exactly 90 ÷ 4.

(a) 00010110 = 22. ✓
(b) 90 ÷ 4 = 22.5. ✓
A 1 (the bit with place value 2) was shifted out and lost, so the remainder is lost. ✓

Analysis

[3 marks]

The value 10010110 is shifted left 1 place to multiply it by 2. Give the result and explain why it is not correct.

Result 00101100 (44). ✓
150 × 2 = 300, which is too big for 8 bits. ✓
The most significant bit, a 1 worth 128, was shifted out and lost. ✓

Apply

[2 marks]

State the shift needed to change 00001100 into 00110000 and the effect on the number.

A logical left shift of 2 places. ✓
The number is multiplied by 4 (12 becomes 48). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.