SFWRENG 3X03 Study Guide - Final Guide: Ieee Floating Point, Single-Precision Floating-Point Format, Repeating Decimal
18 Oct 2016
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Document Summary
On paper, a floating point number is described as follows: Where : d1 . d2 dt decimal digit precision base exponent (integer) d t e. In ieee floating point, numbers are described using the following bit patterns: Calculated by e + 127, represented in binary. (e + 1023 for double precision) Composed of implicit leading bit (1) and fraction. Since we are using binary, we can always rearrange the representation of a number so that it begins with a 1. From this we can see why the leading 1 bit is implicit. Therefore, the only numbers we require for the above problem is the fraction (. 01) and the exponent (10). We require binary(2) and binary(0. 5) binary(2) 10 binary(0. 5) 0. 1. There is a simple, step-by-step method for computing the binary expansion on the right-hand side of the point. We illustrate the method by converting the decimal value . 625 to a binary representation:
