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.
Example of determining the binary value of a floating point number
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.