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Number Representation and Floating Point

Sign and magnitude representation

  • 3 things to know
  • A2 Unit 4

Overview

Recall questions on how the sign bit works, representing −20 and reading 10000111, the range and why it is one value narrower, the two zeros and why they cost, why plain addition fails, and why two's complement displaced it.

What you need to know

Answer each one before you reveal it.

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Key term

How does sign and magnitude represent a negative number, and what does that arrangement cost?

Key term

How does sign and magnitude represent a negative number?

Key term

State the range of an 8-bit sign and magnitude number.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How does sign and magnitude represent a negative number?

    Model answer

    The most significant bit is used as a sign, 0 for positive and 1 for negative, and the remaining bits hold the magnitude.

  2. 2

    Represent −20 in 8-bit sign and magnitude.

    Model answer

    10010100.

  3. 3

    What denary value is 10000111 in 8-bit sign and magnitude?

    Model answer

    −7.

  4. 4

    State the range of an 8-bit sign and magnitude number.

    Model answer

    −127 to +127.

  5. 5

    Give the two representations of zero in 8-bit sign and magnitude.

    Model answer

    00000000 and 10000000.

  6. 6

    Why is having two zeros a problem for a processor?

    Model answer

    A comparison for zero must test two patterns, which complicates the hardware and the programmer's logic.

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