CSCI 2400 Lecture 4: Slides 04
9 Feb 2019
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Document Summary
Bits to right of binary point represent fractional powers of 2. Divide by 2 by shifting right (unsigned) Numbers of form 0. 11111111 are just below 1. 0. 1/2 + 1/4 + 1/8 + +1/2 + (cid:736) 1. 0. Can only exactly represent numbers of the form x/2. Just one setting of binary point within the w bits. Established in 1985 as uniform standard for floating point arithmetic. Some cpus don"t implement ieee 754 in full e. g. , early gpus, cell be processor. Numerical analysis predominated over hardware designers in defining standard. Sign bit s determines whether number is negative or positive. Significand m normally a fractional value in range [1. 0, 2. 0) Exponent e weights value by power of two. Exp field encodes e (but is not equal to e) Frac field encodes m (but is not equal to m) When: exp 000 0 and exp 111 1. Exponent coded as a biased value: e = exp - bias.
