levo

Number Systems and Binary Arithmetic

Logical and arithmetic shifts

  • 3 things to know
  • Component 2

Overview

Logical shift, arithmetic shift and circular shift.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

What is a logical shift?

Key term

Apply a logical left shift of two places to 00010110.

Key term

Apply a logical right shift of one place to 10011010.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is a logical shift?

    Model answer

    A logical shift moves every bit a fixed number of places left or right. Zeros are fed in at the vacated end and bits shifted out are lost.

  2. 2

    Apply a logical left shift of two places to 00010110.

    Model answer

    A logical left shift of two places gives 01011000. Denary 22 becomes 88, because two left shifts multiply by 4.

  3. 3

    Apply a logical right shift of one place to 10011010.

    Model answer

    A logical right shift of one place gives 01001101. Denary 154 becomes 77, which is 154 halved.

  4. 4

    What is an arithmetic shift?

    Model answer

    An arithmetic shift treats the pattern as a signed two's complement number. On a right shift the sign bit is copied into the vacated position.

  5. 5

    Apply an arithmetic right shift of one place to 11110000.

    Model answer

    An arithmetic right shift of one place gives 11111000. Denary −16 becomes −8, which is −16 halved.

  6. 6

    Shift 11011000 right two places, once logically and once arithmetically.

    Model answer

    A logical shift gives 00110110, which is 54 unsigned. An arithmetic shift gives 11110110, which is −10 signed.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Data Structures: Arrays, Records and Hash Tables
Stacks, Queues, Linked Lists and Trees
Boolean Logic and Simplification
Algorithms, Pseudo-Code and Programming Constructs

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

KDW to HAT.
decryptsencryptscompresses

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe two are not the same.
BOpen source refers to the availability of the code.
CMuch open source software is free of charge.

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Backup means the copy of the data.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Number Systems and Binary Arithmetic, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.