CMPT 295 Lecture Notes - Lecture 13: Ieee Floating Point, Significand, Gigabyte

• School: Simon Fraser University
• Department: Computing Science
• Course: CMPT 295
• Professor: Brad Bart

Document Summary

Given n bits, u get at most 2n representations. Step out of range, you lose precision e. g. 2147483647 + 1 = -2147483648. The number of digits determines the precision of the representation e. g. a common situation in decimal (cid:1005)/(cid:1007) = (cid:1004). (cid:1007)(cid:1007)(cid:1007)(cid:1007)(cid:1007)(cid:1007)(cid:1007)(cid:1007) . (cid:1006)/(cid:1007) = (cid:1004). (cid:1010)(cid:1010)(cid:1010)(cid:1010)(cid:1010)(cid:1010)(cid:1010)(cid:1010) . Its easy if you have an infinite amount of paper. Switch encoding to something more precise e. g. rational datatype. A convention to represent the significant digits of numbers and their magnitudes e. g. 6. 022 x 1023 atoms/mol = na (avogadro"s constant) 2. 99792458 x 1023 m/s = c (speed of light) Common usage: normalize exp so one nonzero significant digit precedes the radix point. Composed of 32 bits (64 bits for double) 1 bit for sign: 0/1 <=> +/- (sign magnitude) 8 bits for exponent: range: [-126, 127] represented as 0000 0001 (-126) --> 1111 1110 (127) Encodings 0000 0000 and 1111 1111 handle some edge cases.