You are given that

z = (314; 159; 265; 358)10 = (100100100100101010110011111011001001110)2 :

(a) Is z exactly representable on a VAX-11 as a single precision floating
point number?

(b) Consider also the double precision case, were an additional 32 bits are
appended at the end of the single precision mantissa.

(c) What binary numbers are actually stored in both cases using round-ing.

The following example, of rounding a binary number, from say 3 binary
digits to 2 may be found useful:
0.000 ! 0.00
0.001 ! 0.01
0.010 ! 0.01
0.011 ! 0.10
0.100 ! 0.10
0.101 ! 0.11
0.110 ! 0.11
0.111 ! 1.00

hmmn.. oro yi so si mi lenu,o buyo si

HarkymTheOracle:
hmmn.. oro yi so si mi lenu,o buyo si