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Number Representation and Floating Point

Converting between real numbers and floating point

  • 3 things to know
  • A2 Unit 4

Overview

Recall questions on normalising 0.5, 0.75, 6 and −0.5 into mantissa and exponent, reading a value back from a stored pair, which way the exponent moves as the point moves, why 0.1 cannot be held exactly, and how a negative exponent is represented.

What you need to know

Answer each one before you reveal it.

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Key term

Express 0.5 as a normalised mantissa and exponent.

Key term

Give the 8-bit two's complement mantissa and 8-bit exponent for 0.5.

Key term

Express 6 in normalised floating point form.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Express 0.5 as a normalised mantissa and exponent.

    Model answer

    A mantissa of 0.1 and an exponent of 0.

  2. 2

    Give the 8-bit two's complement mantissa and 8-bit exponent for 0.5.

    Model answer

    Mantissa 01000000, exponent 00000000.

  3. 3

    Express 6 in normalised floating point form.

    Model answer

    0.11 × 2³, so a mantissa of 0.11 and an exponent of 3.

  4. 4

    Give the 8-bit mantissa and 8-bit exponent for 6.

    Model answer

    Mantissa 01100000, exponent 00000011.

  5. 5

    Express 0.75 in normalised floating point form.

    Model answer

    0.11 × 2⁰, so a mantissa of 0.11 and an exponent of 0.

  6. 6

    What real number is held by mantissa 01010000 with exponent 00000010?

    Model answer

    2.5, since 0.101 × 2² is 10.1 in binary.

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