Floating-Point Representation

This lesson covers how computers represent real numbers using floating-point representation. You need to understand the mantissa and exponent, normalisation, converting between floating-point and denary, and the trade-off between precision and range.

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Why Floating-Point?

Fixed-point binary has a fixed binary point position, limiting either range or precision. Floating-point allows the binary point to "float" — move to different positions — enabling representation of very large and very small numbers.

This is similar to scientific notation in denary:

• 3,400,000 = 3.4 x 10^6
• 0.00056 = 5.6 x 10^-4

In binary floating-point:

• The number is stored as a mantissa x 2^exponent

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Structure of a Floating-Point Number

A floating-point number consists of two parts:

Component	Purpose
Mantissa	Stores the significant digits (precision) of the number
Exponent	Stores the power of 2 (determines where the binary point sits)

Both the mantissa and exponent are stored in two's complement so that negative values can be represented.

Example Format: 8-bit Mantissa, 4-bit Exponent