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Consider the following two 16-bit floating-point representations 1. Format A There is one sign bit. There are k = 6 exponent bits. The exponent bias

Consider the following two 16-bit floating-point representations 1. Format A

There is one sign bit.

There are k = 6 exponent bits. The exponent bias is 31.

There are n = 9 fraction bits.

2. Format B

There is one sign bit.

There are k = 5 exponent bits. The exponent bias is 15.

There are n = 10 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 rounding is necessary, you should round toward +. 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 17/26).

Format A Format B
Bits Value Bits Value
0 100001 110100000 29/4 0 10001 1101000000 29/4
1 000000 011100100

0 000000 001011100

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