How overflow can be detected when adding two numbers in 4-bit two’s complement
representation?
A. If you add two different sign numbers, overflow will _____
B. If you add two same sign numbers, overflow will occur if _____
x - y = x + (-y)
C. If you subtract two different sign numbers, overflow will occur if (see B ?)
D. If you subtract two same sign numbers, overflow will (see A ?)
E. A digit-overflow at the MSB is an overflow- is it true? always/sometimes/never
F. If there is no digit-overflow at the MSB, overflow is not possible- is it true? always/
sometimes/ never
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A. If you add two different sign numbers, overflow will sometimes occur. For example, adding a positive number and a negative number can result in an overflow if the magnitude of the sum exceeds the 4-bit range.
B. If you add two same sign numbers, overflow will occur if the resulting sign of the sum does not match the sign of the operands. In other words, if the sum is positive for two negative numbers or negative for two positive numbers, overflow will occur.
C. If you subtract two different sign numbers, overflow will sometimes occur. Just like in the case of adding different sign numbers, subtracting a positive number from a negative number or vice versa can result in an overflow if the magnitude of the difference exceeds the 4-bit range.
D. If you subtract two same sign numbers, overflow will sometimes occur. Similar to adding same sign numbers, subtracting two positive numbers can result in a negative sum that overflows the 4-bit range, or subtracting two negative numbers can result in a positive sum that overflows the range.
E. A digit-overflow at the MSB (Most Significant Bit) is always an overflow. If the result of the addition or subtraction causes the MSB to flip, it indicates that the result cannot be represented in the 4-bit two's complement representation and thus indicates an overflow.
F. If there is no digit-overflow at the MSB, overflow is never possible. If the addition or subtraction result does not cause the MSB to change, it means the sum or difference can be represented within the 4-bit range and no overflow occurs.
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