GCSE · Computer Science · AQA · Spec 8525

Binary shifts

One shift left doubles a number instantly — as long as nothing falls off the end of the register.

What you need to know

  • A left shift by n places multiplies the value by 2ⁿ provided no 1-bits are shifted beyond the register width
  • A right shift by n places divides the value by 2ⁿ (integer division — remainders are lost)
  • Bits shifted beyond the fixed width of the register are discarded and cannot be recovered.
  • Empty bit positions are filled with 0s after a shift

The big picture

A binary shift moves all the bits in a number left or right by a set number of positions. Shifting left multiplies the value by a power of 2 provided no 1-bits are shifted beyond the register width; shifting right divides it, and any remainder is lost. Bits that move beyond the fixed width of the register are discarded and cannot be recovered, and the emptied positions are filled with 0s.

TONIGHT'S REVISION

Binary Shifts

How moving bits left or right multiplies or divides — and what happens when they fall off the edge

Core vocabulary — binary shifts

Get these terms clear first — they come up throughout this topic.

Stop and predict

Commit to an answer before you reveal — this is the moment learning sticks.

An 8-bit register holds 10000000 (decimal 128). A student left-shifts it by 1 place. What will the decimal result be?

Left shift vs Right shift

Left shift (<<)vsRight shift (>>)

Same mechanism, opposite effects — know which is which before the exam.

Focus

Effect on value

Left shift (<<)

Multiplies by 2 per place shifted, provided no 1-bits are shifted beyond the register width

Right shift (>>)

Divides by 2 per place shifted (integer)

The insight

Direction of shift directly determines whether you multiply or divide — left = larger, right = smaller.

Vacated positions filled with

Left shift (<<)

0s on the right

Right shift (>>)

0s on the left

Risk of data loss

Left shift (<<)

Significant bits shifted beyond the left edge are discarded

Right shift (>>)

Truncation — the remainder of division is silently dropped

Equivalent arithmetic

Left shift (<<)

× 2ⁿ (where n = number of places), provided no 1-bits are shifted beyond the register width

Right shift (>>)

÷ 2ⁿ (integer division, floor result)

Example (8-bit)

Left shift (<<)

00000011 (3) << 2 → 00001100 (12)

Right shift (>>)

00001100 (12) >> 2 → 00000011 (3)

Cross-subject · Exam skill

Mark scheme practice — Binary shifts

Read the question, study the model answer, then compare it with your own.

Question

Explain the effect of performing a left shift on a binary number.

Student answer

A left shift moves all bits to the left by one or more places. Each place shifted multiplies the value by 2, provided no 1-bits are shifted beyond the register width. Zeros fill the vacated positions on the right.

Method marks0/2

Key points

1A left shift multiplies by 2 per place provided no 1-bits are discarded; a right shift divides by 2 per place using integer division.
2Zeros fill the vacated bit positions after every shift
3Bits shifted beyond the fixed width of the register are discarded and cannot be recovered
4Right-shift data loss = remainders are silently discarded (truncated, not rounded)
5A shift is a quick way for a processor to multiply or divide by a power of 2

Worked example

Problem

The 8-bit binary value 00001100 (decimal 12) is left-shifted by 2 places. What is the result in binary and decimal?

🧠

Memory hook

Think of a number on a conveyor belt: slide it left and it doubles, slide it right and it halves — but anything that falls off the belt is gone forever, and once that happens the doubling no longer holds.

★ Exam tip

Questions often give you a binary value and ask for the result after a shift. Write out the shifted bit pattern first, then convert — rather than trying to do both steps at once. Say clearly what happened to any bits that moved beyond the end of the register.

⚠ Watch out

Thinking a right shift rounds to the nearest whole number — it always truncates (floors) the result, so 00000101 (5) right-shifted by 1 gives 00000010 (2), not 3.

Check yourself

Without looking — what is the decimal result of left-shifting 00000011 by 3 places in an 8-bit register, and why?

Flashcards

(22)
What does a left shift by 1 place do to a binary number's value?
It multiplies the value by 2, provided no 1-bits are shifted beyond the register width.
What does a right shift by 1 place do to a binary number's value?
It divides the value by 2 (integer division — remainder discarded).
What fills the vacated bit positions after a shift?
Zeros (0s) fill the empty positions.
What happens to bits shifted beyond the end of a fixed-width register?
When bits are shifted beyond the register's width and are permanently lost.
A left shift by n places multiplies by what?
2ⁿ (2 to the power of n), provided no 1-bits are shifted beyond the register width.
A right shift by n places divides by what?
2ⁿ (integer division).
What is 00000100 left-shifted by 2 in decimal?
00010000 = 16. (4 × 4 = 16)
What is 00010000 right-shifted by 3 in decimal?
00000010 = 2. (16 ÷ 8 = 2)
Why do processors use binary shifts instead of multiplication?
A shift is a quick way to multiply or divide by a power of 2.
What happens to the remainder when a right shift produces a non-integer result?
It is truncated (discarded) — not rounded.
00000101 (decimal 5) is right-shifted by 1. What is the result?
00000010 = decimal 2. (5 ÷ 2 = 2 remainder 1 — remainder lost)
If an 8-bit register holds 11000000 and is left-shifted by 2, what is lost?
The two leading 1-bits are shifted beyond the register width and discarded — that data is lost.
What is 00000001 left-shifted by 7 in an 8-bit register?
10000000 = decimal 128.
What is the binary shift operation that represents ÷ 4?
A right shift by 2 places.
What is the binary shift operation that represents × 8?
A left shift by 3 places.
In which direction do bits shift to multiply a value?
Left.
In which direction do bits shift to divide a value?
Right.
What decimal value does 00001111 right-shifted by 2 give?
00000011 = decimal 3. (15 ÷ 4 = 3 remainder 3 — remainder lost)
What is the term for bits that move beyond the register boundary and are lost?
They are discarded and cannot be recovered.
How many places left would you shift to multiply a number by 16?
4 places (2⁴ = 16).
Does a binary shift work the same way regardless of whether the number is odd or even?
For left shifts, yes. For right shifts, odd numbers lose their least-significant bit (the remainder of ÷2 is dropped).
What is 00110000 right-shifted by 3?
00000110 = decimal 6. (48 ÷ 8 = 6)

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learn Binary shifts properly — interactive practice, marked questions and flashcards.

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