Creating a One Byte Floating Point Number

Introduction

However, to explain how floating point addition and multiplication work, it's nicer to use a much smaller representation for floating point numbers. The additional bits in IEEE 754 single precision would make the examples more difficult to read.

So, we're going to create a 1 byte floating point representation. We'll loosely model it after IEEE 754 single precision.

Here are the specs.

• B₇ is the sign bit.
• B_6-3 is the exponent. There are 4 bits for the exponent, which is represented in excess 7.
• B_2-0 is the fraction. Three bits are used to represent the fraction. There is a hidden 1.
• You can assume there's denormalized numbers, zero, infinity, and NaN, but we won't worry about most of these categories.

Convert -4.5_ten to binary and you get -100.1_two.
Then write it in scientific notation as: - 1.001_two X 2^2_ten.

We can write this in our one byte format as:

Example 2

• Convert 4.25_ten to binary and you get 100.01_two.
  
• Then write it in scientific notation as: 1.0001_two X 2^2_ten.
  
• We need 4 bits after the radix point, but our representation only permits 3 bits, so we either some method for rounding. To make our represenation simple, we simply truncate additional bits. So, the result is: 1.000_two X 2^2_ten.
  
• Using our one byte floating point representation, the value is represented as:

  sign	exponent	fraction
  1	1001	000

On Your Own

Web Accessibility