-4095 sign 1, exponent 5, significand 10
A. Treat as unsigned and convert to binary
4095
2047 1
1023 1
511 1
255 1
127 1
63 1
31 1
15 1
7 1
3 1
1 1
0 1 1111 1111 1111b
B. no .decimal portion
C. Adjust the binary value to scientific style notation.
1.111 1111 1111 x 2^11
D. Calculate the bias for the exponent
2^(5-1)-1 = 2^4-1 = 16-1 = 15
E. Add bias to exponent and covert to binary
15 + 11 26
26
13 0
6 1
3 0
1 1
0 1 11010
F.
Sign negative so sign bit 1
Biased exponent 11010
Find significand
Most significant bit 1. not stored
And float can hold only 10 significant digits, so we store only the most
significant portion.
1.111 1111 1111
^ ^^^ ^^^^ ^^^
h 10 digits
i
d
d
e
n
1 11010 111 1111 1111