Question

Consider the following example: MOV AL, −5 SUB AL, +125 After executing these two lines of instructions, Carry Flag, CF=0 and overflow flag, OF =1. Show appropriate computation and reasoning to explain why CF=0 and OF=1. -

Answer 1

After executing the MOV and SUB instructions on an 8-bit register, the OF is set to 1 due to an arithmetic overflow while the CF is 0 because there's no carry-out from the most significant bit, indicating no passage beyond the maximum representable positive value.

Step-by-step explanation:

To understand why in the instructions

• MOV AL, -5
• SUB AL, +125

the Carry Flag (CF) is 0 and the Overflow Flag (OF) is 1, we need to consider how the CPU handles arithmetic operations, specifically with 8-bit registers like AL in the x86 architecture. For the MOV instruction, AL is loaded with the 8-bit two's complement representation of -5, which is 0xFB in hexadecimal (11111011 in binary). The SUB instruction then attempts to subtract +125, which is 0x7D in hexadecimal (01111101 in binary), from this value.

Here's the binary arithmetic computation:

• 11111011 (-5 in binary)
• 10000011 (Negative of +125 in binary, after two's complement conversion)
• ---------
• 01111110 (Result of binary addition, interpreted as +126 rather than -130 due to overflow)

Since the result, 01111110, represents a positive value and the addition of two's complement values has gone beyond the range of an 8-bit register (-128 to +127), an overflow has occurred, which sets the OF to 1. The CF, on the other hand, is cleared to 0 because there was no carry-out from the most significant bit in the arithmetic operation, which would indicate that we've passed the maximum positive value that can be represented in an 8-bit register.