CSE431 Chapter 3.20Irwin, PSU, 2008 IEEE 754 FP Standard  Most (all ) computers these days conform to the IEEE 754 floating point standard (-1) sign x (1+F) x 2 E-bias l Formats for both single and double precision l F is stored in normalized format where the msb in F is 1 (so there is no need to store it!) – called the hidden bit l To simplify sorting FP numbers, E comes before F in the word and E is represented in excess (biased) notation where the bias is -127 (-1023 for double precision) so the most negative is 00000001 = 2 1-127 = 2 -126 and the most positive is 11111110 = 2 254-127 = 2 +127  Examples (in normalized format) l Smallest+: 0 00000001 1.00000000000000000000000 = 1 x 2 1-127 l Zero: 0 00000000 00000000000000000000000 = true 0 l Largest+: 0 11111110 1.11111111111111111111111 = 2-2 -23 x 2 254-127 l 1.0 2 x 2 -1 = l 0.75 10 x 2 4 =
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