Question

Given the following table of 5 numeric values (listed both in hexadecimal and 8-bit binary representation). Answer the questions below, using the ID to identify the number you wish to specify as the correct answer.

Num1 FF 1111 1111
Num2 07 0000 0111
Num3 F8 1111 1000
Num4 87 1000 0111
Num5 80 1000 0000
a. Which of the above 5 numbers is the largest 8-bit unsigned binary number
b. Which of the above 5 numbers is equivalent to the same base 10 number when it is interpreted by a computer using signed-magnitude representation and a computer using 2's complement representation?
c. Suppose Num 3 is interpreted as a 1's complement numbers. Which of the following numbers corresponds to the signed-magnitude representations of the same number?
d. Which of the above 5 numbers is the largest 8-bit 2's complement?
e. Which of the above 5 number is the smallest 8-bit 2's complement number?
f. Which of the above 5 numbers is the smallest 8-bit signed magnitude number?

Answer 1

Num3 is the largest 8-bit unsigned binary number. Num1, Num3, and Num4 are equivalent in signed-magnitude and 2's complement representation. Num3 is the largest 8-bit 2's complement number. Num4 is the smallest 8-bit 2's complement number. Num5 is the smallest 8-bit signed magnitude number.

Step-by-step explanation:

1. a. Num3 is the largest 8-bit unsigned binary number because it is represented by the hexadecimal value F8, which translates to 1111 1000 in binary. This is larger than any of the other values.
2. b. Num1, Num3, and Num4 are equivalent to the same base 10 number when interpreted by a computer using signed-magnitude representation and 2's complement representation.
3. c. If Num3 is interpreted as a 1's complement number, the corresponding signed-magnitude representation would be -7, equivalent to Num4.
4. d. Num3 is the largest 8-bit 2's complement number because it has the most significant bit set to 1.
5. e. Num4 is the smallest 8-bit 2's complement number because it has the most significant bit set to 1.
6. f. Num5 is the smallest 8-bit signed magnitude number because it has the most significant bit set to 1.