4.1.17

Floating Point Subtraction

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Floating Point Subtraction

When subtracting 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.

Subtraction

Subtraction

  • The example below shows the subtraction 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
Two's complement

Two's complement

  • The next step is to find the twos complement of the second number:
    • 1.1001000
Add mantissas

Add mantissas

  • The two mantissas can then be added:
    • 0.1011000 + 1.1001000 = 0.1000000
  • Note that the first digit of the two's complement corresponds to -1 in decimal.
  • Factor this in when you do the addition.
Normalise the result

Normalise the result

  • The result should then be normalised by moving the binary point one place to the left.
  • That means we add 1 to the exponent:
    • 1.00100000100
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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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2.2

Applications Generation

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2.3

Software Development

2.3.1Algorithmic Thinking2.3.2Waterfall Lifecycle2.3.3Waterfall Lifecycle - Strengths & Weaknesses2.3.4Agile Methodology2.3.5Agile Methodology - Strengths & Weaknesses2.3.6Extreme Programming2.3.7Extreme Programming - Strengths & Weaknesses2.3.8Spiral Methodology2.3.9Spiral Methodology - Strengths & Weaknesses2.3.10Rapid Application Development2.3.11RAD - Strengths & Weaknesse
2.4

Types of Programming Language

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3

Exchanging Data

3.1

Compression, Encryption & Hashing

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3.2

Databases

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3.3

Networks

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Web Technologies

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4

Data Types, Data Structures & Algorithms

4.1

Data Types

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4.2

Data Structures

4.2.13D Arrays4.2.2Linked List4.2.3Queues4.2.4Graphs4.2.5Hash Tables4.2.6Stacks4.2.7Trees4.2.8Binary Search Trees
4.3

Boolean Algebra

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5

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5.1

Computing Related Legislation

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5.2

Moral & Ethical Issues

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6

Elements of Computational Thinking

6.1

Thinking Abstractly

6.1.1Abstraction
6.2

Thinking Ahead

6.2.1Inputs & Outputs
6.3

Thinking Procedurally

6.3.1Decomposition
6.4

Thinking Logically

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6.5

Thinking Concurrently

6.5.1Concurrent Processing
7

Problem Solving & Programming

7.1

Programming Techniques

7.1.1Variables & Constants7.1.2Comments7.1.3Inputs & Outputs7.1.4Subroutines7.1.5Scope
7.2

Programming Construction

7.2.1Integrated Development Environments7.2.2The Purpose of Testing7.2.3Types of Testing7.2.4Test Plans
8

Algorithms

8.1

Algorithms

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Practice questions on Floating Point Subtraction

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Floating Point Addition

Bitwise Manipulation - Shifts