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?
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.
Key points
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?
What does a right shift by 1 place do to a binary number's value?
What fills the vacated bit positions after a shift?
What happens to bits shifted beyond the end of a fixed-width register?
A left shift by n places multiplies by what?
A right shift by n places divides by what?
What is 00000100 left-shifted by 2 in decimal?
What is 00010000 right-shifted by 3 in decimal?
Why do processors use binary shifts instead of multiplication?
What happens to the remainder when a right shift produces a non-integer result?
00000101 (decimal 5) is right-shifted by 1. What is the result?
If an 8-bit register holds 11000000 and is left-shifted by 2, what is lost?
What is 00000001 left-shifted by 7 in an 8-bit register?
What is the binary shift operation that represents ÷ 4?
What is the binary shift operation that represents × 8?
In which direction do bits shift to multiply a value?
In which direction do bits shift to divide a value?
What decimal value does 00001111 right-shifted by 2 give?
What is the term for bits that move beyond the register boundary and are lost?
How many places left would you shift to multiply a number by 16?
Does a binary shift work the same way regardless of whether the number is odd or even?
What is 00110000 right-shifted by 3?
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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