I would like a step by step explanation as to how the 7-bit floating point representations from Format A were converted to Format B. Thanks.

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 non-negative numbers.

i). Format A.

There are k=3 exponent bits. The exponent bias is 3.

There are n=4 fraction bits.

ii). 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 or 17/2).

Format A Format B

Bits	Value	Bits	Value
011 0000	1	0111 000	1
101 1110	15/2	1001 111	15/2
010 1001	25/32	0110 100	3/4 (Round down)
110 1111	31/2	1011 000	16 (Round up)
000 0001	1/64	0001 000	1/64 (Denormalize -> normalized)