Question

2. Represent 25.28255 in 32 bit IEEE-754 floating point format as shown in the following format discussed in class. Sign Bit BIT 31 Exponent BITS 30:23 Mantissa BITS 22:0 BYTE 3+1 bit 7 Bits BYTE 1 BYTE O

Answer 1

Given :- 25.292.55 first take 25, we can write 25 08 as 12 = 6 * 2 + 6 = 3 *9.to W.mite down the last nombuses - 3 = x2 + 1 from bottom to top 1.0 x 2 +11 We get 25 of 11ool in binany famat Now we convent 0.28255, 0.28 255 x 2 = 0.5651 0.5651 X 2 1.1 302 0.1302 x 2 - 0 2604 0.2604 x 2 0.52208 0.5208 x 2 = 1.0416 0.0416 X 2 =0.0832 0.1664 0.0832 0.1664 x2 = 0.3328 0.3328 * 2 506656 0.6656 * 2 = 1 3.312 0. 3312 x 2 = 0.6624

0.6624 x 2 1.3248 0 3248 * 2 0.6496 0.6496 x 2 = 1.2992 0.2992 X 2 = 0.59814 0.5984 x 2 = 1:1968 0.1968 X 2 =0.39 36 0.3936 x 2 = 0.7872 72 x 2 = 1.57444 44 x 2 = 1.1488 88 x 2 = 0.2976 0.78 - 0 2976 x =0.5952 0.5952 x = 1:1904 0.1904 x 2 = 0.3808 Now we write it as (25.26255)= (11001101001000010101010011001), Now we move the decimal point, then we get tool 0100100001010101001100 X 27

Sign, SEO [ +ve number] Exponent, E = 4 Mantissa, M = 10010100100001010101001101 Now writing Exponent valere as 8 Bit Exponential .: E. 4 , C., 127 +4 = 131 Мало тераздевод 131 in bicoxy ыe at (131) E (10000011), 10 This is the actual value that is going to 'be our Exportent Bits. Format: Sign Bit Bit 31 B EXPONENT BIT 30:23 MANTISSA BITS 2210 10000011 10010100100001010101001
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