Question

17. If the following uses the floating-point format defined in Figure 1.25 of the textbook, what is the decimal notation for this number: 01100101

18. Encode the following decimal value using the 8-bit floating-point format of Figure 1.25: 7/8 HINT: Be sure to use the normalized form. Note: Answer should be in the format n nnn nnnn

19. Encode the following decimal value using the 8 bit floating point format of Figure 1.24: 7/8 (HINT: be sure to use the normalized form.) Note: answer should be in the format of "n nnn nnnn"

Answer 1

17)
0 110 0101

sign bit is 0. so, it's positive.
bias is 3.
exponent bits are 110. In decimal it is 6.
frac bits are 0101
so, in decimal 0 110 0101 is +1.0101 * 2^3
=>  1010.1
=>  In decimal this is 10.5
Answer: 10.5

18)
7/8 =>  0.875
0.875 in simple binary => 0.111
so, 0.875 in normal binary is 0.111 => 1.11 * 2^-1

sign bit is 0(+ve)
exp bits are (3-1=2) => 010
frac bits are 1100

so, 0.875 in 8-bit format is 0 010 1100
Answer: 0 010 1100

19)
This question is exactly as same as 18