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Data, Information and Data Representation

Two's complement and negative numbers

  • 3 things to know
  • AS Unit 2

Overview

Why a sign bit alone is not enough, forming a negative value by inverting and adding one, reading a negative pattern back, the range from −128 to 127, and adding a negative to a positive.

What you need to know

Answer each one before you reveal it.

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Key term

Why is a special system needed to hold negative numbers in binary?

Key term

In an 8-bit two's complement number, what does the leftmost bit tell you?

Key term

What range of values can 8-bit two's complement represent?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Why is a special system needed to hold negative numbers in binary?

    Model answer

    A plain binary pattern carries no minus sign, so an agreed convention is needed that lets the same eight bits stand for negative values as well as positive ones.

  2. 2

    In an 8-bit two's complement number, what does the leftmost bit tell you?

    Model answer

    The leftmost bit is the sign bit, and a 0 there means the number is positive or zero while a 1 means it is negative.

  3. 3

    What range of values can 8-bit two's complement represent?

    Model answer

    Eight-bit two's complement represents every whole number from −128 to +127.

  4. 4

    Why does the range reach one further below zero than above it?

    Model answer

    The pattern of all zeros is used for zero itself, which leaves 127 patterns for positive values and 128 patterns for negative ones.

  5. 5

    Describe the procedure for writing a negative number in 8-bit two's complement.

    Model answer

    The size of the number is written as an 8-bit positive binary value, every bit is then inverted, and 1 is added to the inverted pattern.

  6. 6

    What is −5 in 8-bit two's complement?

    Model answer

    The value −5 is 11111011, found by writing 5 as 00000101, inverting that to 11111010 and adding 1.

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