levo

Number Systems and Binary Arithmetic

Binary and denary place value

  • 3 things to know
  • Component 2

Overview

Base of the binary number system, repeated division method for converting denary to binary and how you check a denary to binary conversion.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

What is the base of the binary number system?

Key term

State the place values of the eight columns in an 8-bit binary number.

Key term

Convert binary 11010110 to denary.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the base of the binary number system?

    Model answer

    Binary is a base 2 system using only the digits 0 and 1. Each column is worth twice the column to its right.

  2. 2

    State the place values of the eight columns in an 8-bit binary number.

    Model answer

    The eight columns are worth 128, 64, 32, 16, 8, 4, 2 and 1. Each value is a power of two, from 2⁷ down to 2⁰.

  3. 3

    Convert binary 11010110 to denary.

    Model answer

    Binary 11010110 is 214 in denary. The set bits are worth 128, 64, 16, 4 and 2, which sum to 214.

  4. 4

    Convert denary 200 to 8-bit binary.

    Model answer

    Denary 200 is 11001000 in binary. The value comes from 128 plus 64 plus 8.

  5. 5

    Convert denary 45 to 8-bit binary.

    Model answer

    Denary 45 is 00101101 in binary. The set columns are 32, 8, 4 and 1.

  6. 6

    Describe the repeated division method for converting denary to binary.

    Model answer

    The denary number is divided repeatedly by 2 and each remainder is recorded. The remainders read from last to first give the binary pattern.

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.