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Data Representation and Data Types

The binary number system

  • 3 things to know
  • AS Unit 1

Overview

Column values in an eight-bit binary number, largest value eight bits can hold as an unsigned number and largest unsigned value that fits in sixteen bits.

What you need to know

Answer each one before you reveal it.

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Key term

Describe the column method for converting denary to binary.

Key term

What are the column values in an eight-bit binary number?

Key term

Convert 10110110 in binary to denary.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What are the column values in an eight-bit binary number?

    Model answer

    Reading from the right they are 1, 2, 4, 8, 16, 32, 64 and 128, that is 2⁰ up to 2⁷, each double the one to its right.

  2. 2

    Convert 10110110 in binary to denary.

    Model answer

    The set columns are 128, 32, 16, 4 and 2, which add to 182.

  3. 3

    Convert 200 in denary to eight-bit binary.

    Model answer

    Taking 128, then 64, then 8 accounts for the whole value, giving 11001000.

  4. 4

    Convert 45 in denary to eight-bit binary.

    Model answer

    The columns 32, 8, 4 and 1 add to 45, giving 00101101.

  5. 5

    Convert 00111111 in binary to denary.

    Model answer

    The set columns are 32, 16, 8, 4, 2 and 1, which add to 63.

  6. 6

    What is the largest value eight bits can hold as an unsigned number, and why?

    Model answer

    It is 11111111 in binary, which is 255 in denary, because eight bits give 2⁸ = 256 patterns and the counting starts at zero.

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