10.
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Using 8-bit integers, what is the final result of the following operations: NOT((0x8 OR 128) + 1) XOR 15
Note:
- AND = "logical and" operator
- OR = "logical or" operator
- XOR = "logical exclusive or" operator
- NOT = "logical not" operator
- 0x = hexadecimal numbers
- + = Arithmetic addition operator
Pick ONE option
Show answer & explanation
Answer: A. 0x79
The problem requires evaluating a sequence of bitwise and arithmetic operations on 8-bit integers. The key is to correctly handle the 8-bit overflow during addition and the bitwise NOT (one's complement) operation.
Step-by-step Derivation:
Step-by-step calculation:
0x8 OR 128:
- 0x8 in binary (8-bit): 0000 1000
- 128 in binary (8-bit): 1000 0000
- 0000 1000 OR 1000 0000 = 1000 1000 (which is 136 in decimal).
(0x8 OR 128) + 1:
- 1000 1000 + 0000 0001 = 1000 1001 (which is 137 in decimal).
NOT(1000 1001):
- Bitwise NOT flips all bits: NOT(1000 1001) = 0111 0110.
- 0111 0110 in hex is 0x76 (Decimal 118).
0x76 XOR 15:
- 0x76 in binary: 0111 0110
- 15 in binary: 0000 1111
XOR operation:
0111 1001
0111 0110
0000 1111
Convert result to Hex:
- 0111 1001 binary = 0x79 hex.
Final Result: 0x79