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Data Types, Characters and Floating Point

Truncation, rounding and accuracy

  • 3 things to know
  • Component 2

Overview

Absolute error, relative error and danger of subtracting two nearly equal floating point numbers.

What you need to know

Answer each one before you reveal it.

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Key term

Define truncation.

Key term

Define rounding.

Numbers

Truncate the binary fraction 0.1011101 to four places after the point and give the denary value.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define truncation.

    Model answer

    Truncation cuts off the digits beyond the available precision. The digits that remain are left exactly as they were.

  2. 2

    Define rounding.

    Model answer

    Rounding is the adjustment of the last digit kept according to the first digit discarded. The stored value is the closest representable value to the true one.

  3. 3

    Truncate the binary fraction 0.1011101 to four places after the point and give the denary value.

    Model answer

    Truncation to four places gives 0.1011, which is 0.6875 in denary. The true value 0.1011101 is 0.7265625, so the error is 0.0390625.

  4. 4

    Round the binary fraction 0.1011101 to four places after the point and give the denary value.

    Model answer

    The fifth bit is 1, so the fourth bit rounds up to give 0.1100. The stored value is 0.75 in denary and the error is 0.0234375.

  5. 5

    Which of truncation and rounding is more accurate, and why?

    Model answer

    Rounding is more accurate, because the error is at most half a unit in the last place. Truncation can lose almost a whole unit in the last place.

  6. 6

    Why is truncation still used despite being less accurate?

    Model answer

    Truncation simply discards the surplus bits and needs no extra arithmetic. Speed and simplicity matter in hardware that performs millions of operations.

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