How to Determine the Binary Value from a Single-precision Floating Point Representation

In the previous article, we have seen the representation of a binary number in IEEE 754 single-precision floating point format. In this article, we will do the reverse process, which means determining the value of a binary number from a floating-point representation. For this, we will use the following formula:

Binary Number = (-1)S(1 + F)(2E-127)

Example:

Consider a number represented in IEEE 754 single-precision floating point format is 11001001111100100010000000000000. Determine the value of the binary number.

Solution:

Let’s break the given number into sign, exponent, and mantissa as below.

The sign bit is ‘1’, so the number is a negative number.

Biased exponent value, E = 10010011₂ = 147₁₀

Mantissa part, F = .11100100010000000000000

So, 1+F = 1.1110010001

Now, applying the above-given formula:

Binary Number = (-1)1(1.1110010001)(2147-127) = (-1)(1.1110010001)(220) = -111100100010000000000

The equivalent decimal value of the given floating point number is -19,83,488.

In the next article, we will learn how to find the floating point value of a decimal fractional number.

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