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

The largest 8-bit unsigned binary number is Num1 (FF). Num2 is equivalent in both signed-magnitude and 2's complement representations. The largest 8-bit 2's complement number is Num4 (87). The smallest 8-bit 2's complement number and the smallest 8-bit signed magnitude number is Num5 (80).

Step-by-step explanation:

a. Which of the above 5 numbers is the largest 8-bit unsigned binary number?

The largest 8-bit unsigned binary number is Num1, which is FF in hexadecimal and 11111111 in binary.

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?

The number that is equivalent in both signed-magnitude and 2's complement representations is Num2, which is 07 in hexadecimal and 00000111 in binary.

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?

When Num3 is interpreted as a 1's complement number, the corresponding signed-magnitude representation is -7F, where F8 in hexadecimal is 11111000 in binary.

d. Which of the above 5 numbers is the largest 8-bit 2's complement?

The largest 8-bit 2's complement number is Num4, which is 87 in hexadecimal and 10000111 in binary.

e. Which of the above 5 numbers is the smallest 8-bit 2's complement number?

The smallest 8-bit 2's complement number is Num5, which is 80 in hexadecimal and 10000000 in binary.

f. Which of the above 5 numbers is the smallest 8-bit signed magnitude number?

The smallest 8-bit signed magnitude number is Num5, which is 80 in hexadecimal and 10000000 in binary.