Consider the following two 7-bit floating-point representations based on the IEEE floating-point format. Neither has a sign bit—they can only represent nonnegative numbers.

1. Format A
There are k = 3 exponent bits. The exponent bias is 3.
There are n = 4 fraction bits.

2. Format B
There are k = 4 exponent bits. The exponent bias is 7.
There are n = 3 fraction bits.

Below, you are given some bit patterns in format A, and your task is to convert them to the closest value in format B. If necessary, you should apply the round to-even rounding rule. In addition, give the values of numbers given by the format A and format B bit patterns. Give these as whole numbers (e.g., 17) or as fractions (e.g., 17/64).

Transcribed Image Text:

Format A Bits 011 0000 101 1110 010 1001 110 1111 000 0001 Value 1 Format B Bits 0111 000 Value 1