[Cst-1b] numerical analysis 98/3/10

[Phebe Mann]

Thanks for the suggestions.

IEEE 754 standard  :- 
sign | exponent | significand
1bit  | 8 bits  | 23 bits

I think 1.125 x 2^-31's bit pattern should  be :
0|01100000|0010....0

and not
0|00100000|00...1100000

similarly
The bit pattern for smallest representable number greater than 2^16
0|1000111|00....01

The decimal value is  (1+2^-23) x 2^16 = 2^16 + 2^23 < 2^17

and not 
(1+2^-8) x 2^16 = 2^16 + 2^8 < 2^17


Phebe


On Tue, 30 May 2000, M.Y.W.Y.B. wrote:

> --On Dienstag, 30. Mai 2000, 10:37 +0100 "Phebe Mann"
> <pm258@hermes.cam.ac.uk> wrote: 
> 
> > 
> > 98/3/10
> > 
> > What are the bit patterns for :-
> > 
> > 1) 1.125 x 2^-31 (significand) and how to get it ?
> 
> 1.125 = 1 + 1/8 = 1 + 1/2^3
> ie in binary 1.001
> so the bit pattern is 00100000
> The bit pattern of the exponent is -31 + 127 = 96 = 1100000 binary
> So the entire bit pattern is 
> 0|00100000|00...1100000
> 
> > 2) small representable number greater than 2^16 (exponent &
> > significand) and how to get it ?
> 
> The exponent of 2^16 has the pattern 16 + 127 = 15 + 128 = 10001111 binary
> The significand of 2^16 has pattern 00...00
> 
> So the smallest number > 2^16 has significand 00..01 and the same exponent.
> 
> The decimal value is (1+2^-8) x 2^16 = 2^16 + 2^8 < 2^17
> 
> 
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