4.1.16

Floating Point Addition

Test yourself

Floating Point Addition

When adding floating point binary numbers, it is important to ensure each number is represented with the same level of precision. This means that the exponents must be the same.

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Addition

  • The example below shows the addition of two normalised 12-bit floating point numbers, with 8-bit mantissas and 4-bit exponents:
    • 0.10110000011 + 0.11100000010
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Matching exponents

  • The first step is to ensure the exponents of the two numbers match, by adding 1 to the exponent of the second number (2) to match that of the first (3).
  • Adding 1 to the exponent of the second number moves the binary point of the mantissa in this number one place to the left:
    • 0.11100000010 →\rightarrow 0.01110000011
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Compute the addition

  • The two mantissas can then be added together:
    • 0.1011000 + 0.0111000 = 1.0010000
  • Including the exponent gives 1.00100000011.
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Normalise the result

  • Check that the result is normalised, and move the binary point as necessary.
  • If the binary point gets moved, remember to change the exponent accordingly.

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1Components of a Computer

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4.1.16Floating Point Addition

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Normalisation of Floating Points

Floating Point Subtraction