Chapter 2, Problem 40E

a.

Explanation of Solution

Decimal equivalent for “0 10000000 00000000000000000000000”:

• The given floating point number is “0 10000000 00000000000000000000000”.
• The LSB is “0” and this denotes a positive number.
• The next eight bits denotes the unsigned integer “128”.
• If “127” is subtracted from “128”, then the actual exponent is “1”.
• The next “23” bits in the fraction field contains “0”.
• Therefore, the decimal number being expressed is “$+1$

b.

Explanation of Solution

Decimal equivalent for “1 10000011 00010000000000000000000”:

• The given floating point number is “1 10000011 00010000000000000000000”.
• In the given floating point number, the leading bit is “1” and this denotes a negative number.
• The next eight bits denotes the unsigned integer “131”.
• If “127” is subtracted from “131”, then the actual exponent is “4”...

c.

Explanation of Solution

Decimal equivalent for “0 11111111 00000000000000000000000”:

• The given floating point number is “0 11111111 00000000000000000000000”.
• In the given floating point number, the leading bit is “0” and this denotes a positive number...

d.

Explanation of Solution

Decimal equivalent for “1 10000000 10010000000000000000000”:

• The given floating point number is “1 10000000 10010000000000000000000”.
• In the given floating point number, the leading bit is “1” and this denotes a negative number.
• The next eight bits denotes the unsigned integer “128”.
• If “127” is subtracted from “128”, then the actual exponent is “1”...