What decimal value does the 8-bit binary number 00010001 have if: a) It is inter

Question

What decimal value does the 8-bit binary number 00010001 have if: a) It is interpreted as an unsigned number? b) It is on a computer using signed-magnitude representation? c) It is on a computer using one’s complement representation? 175 d) It is on a computer using two’s complement representation? e) It is on a computer using excess-127 representation? I found the answer here but I feel like that is not correct cause it is giving same answer for questions a. b. c. Can somebody post the right answer please?

Explanation / Answer

8- bit binary = 0001 0001;

a. Unsigned Representation: Answer: 17

Explanation:

If it is unsigned number: 0*27 + 0*26 + 0*25 + 1*24 + 0*23 + 0*22 + 0*21 + 1*20 = 16 + 1 = 17

b. Signed Representation: Answer: 17

Explanation: MSB defines the sign; if MSB is zero then the number is negative, similarly if MSB is positive, then the number is positive.

c. one’s compliment: Answer: 238

Explanation: one’s compliment makes 0 to 1 and 1 to 0. Then the 8 bit number is 11101110 = 1*27 + 1*26 + 1*25 + 0*24 + 1*23 + 1*22 + 1*21 + 0*20 = 128+ 64 + 32 + 8 + 4 + 2 = 238

d. two’s Compliment: Answer: 17

Explanation: 2’s complement If the MSB is 1; then the number should be converted to one’s compliment and then binay; otherwise same as normal binay representation: 0*27 + 0*26 + 0*25 + 1*24 + 0*23 + 0*22 + 0*21 + 1*20 = 16 + 1 = 17

e. Excess 127: Answer: -110;

Explanation: Excees 127 means adding 127 to the number and converting it to binary; Here decima; number is 17 and subtract 127 from 17 which gives -110

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