4.1.16

Floating Point Addition

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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.

Addition

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
Matching exponents

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
Compute the addition

Compute the addition

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

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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1

Components of a Computer

1.1

Structure & Function of the Processor

1.1.1Von Neumann Architecture1.1.2Registers1.1.3Buses1.1.4Fetch, Decode, Execute Cycle1.1.5Factors Affecting CPU Performance1.1.6Pipelining1.1.7CPU Architecture
1.2

Types of Processors

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1.3

Input, Output & Storage

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2

Software & Software Development

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Systems Software

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Applications Generation

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2.3

Software Development

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Types of Programming Language

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3

Exchanging Data

3.1

Compression, Encryption & Hashing

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Databases

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Networks

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Web Technologies

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4

Data Types, Data Structures & Algorithms

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Data Types

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4.2

Data Structures

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4.3

Boolean Algebra

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5

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Computing Related Legislation

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5.2

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6

Elements of Computational Thinking

6.1

Thinking Abstractly

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6.2

Thinking Ahead

6.2.1Inputs & Outputs
6.3

Thinking Procedurally

6.3.1Decomposition
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Thinking Logically

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Thinking Concurrently

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7

Problem Solving & Programming

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Programming Techniques

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Programming Construction

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8

Algorithms

8.1

Algorithms

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Practice questions on Floating Point Addition

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  1. 1
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Normalisation of Floating Points

Floating Point Subtraction