Question

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 (011111) There are n 9 fraction/mantissa bits 2. Format B There is one sign bit There are k 5 exponent bits. The exponent bias is 15 (01111) There are n 10 fraction/mantissa bits Problem 1 (81 points total /3 points per blank) Below, you are given some bit patterns in Format A, and your task is to convert them to the closest value in Format B and vice versa. 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 17/8 or 2 1 /8) NO DECIMALS Format A Format EB Bits 0 100001 110100000 Value 29/4 Bits 0 10001 1101000000 Value 29/4 Q1.1 1 000000 011001100 Q1.2 Q1.3 0 010001 101011100 Q1.4 Q1.5 1 101000 000011100 0 10101 0000000000 0 01010 0000000001 Q1.7 01.8 Q1.90 011011 100100011 0 01101 0000000101 0 00111 0000000001

Please show work, thanks.

Answer 1

Guen Tuo-1b bit d sign bit S bitt, bias -1s sign l, biaed e Sianl cchon 1216 5t 1 28 12-3 135 128 x23 1 .394389534升2

gnbioud exgona 10011139 exponent 39 3 2 3 3 3X2 = 33-3):2 1 6 ar 13

k 1011b0o iloo0oo 95-316 16 1b 3 16496 6ytu 31 1o24 sign bias expnert 00o 1-3)-30 3 19 ใ28425 124 2 15) 12%

2 S 30 -19% 2 IS) 122 13u3 S3ua2 a ane cleet value in Conu 凸 Patern A