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A binary adder-subtractor is a digital circuitry that has the capability of adding or subtracting binary numbers based on a control signal. The adder-subtractor circuit has a switch mode control input that switches the mode of the circuitry between addition and subtraction.

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The switch mode control uses the XOR gate logic. Setting the input control signal to logic zero causes the digital circuit to function as a binary adder and setting the input control signal to logic one causes the digital circuit to function as a binary subtractor.

The adder-subtractor circuit adds or subtracts 8-bit binary numbers using the two?s-complement notation. In this notation system, the most significant bit designates the sign of the number and is not a part of the number value. A value zero in the most significant bit location designates a positive binary number. A value one designates a negative binary number.

A carry-in and carry-out bit in the circuit determines whether an overflow occurs. Adding two positive numbers within the range where the sum is also within the range produces a correct positive result with no carry or no overflow. In the case the sum is beyond range, it signals an overflow.

During two?s-complement subtraction with a negative and a positive number, the sign bit indicates a positive value, there is no overflow and the carry bit gets discarded. Adding two?s-complement negative numbers results in the carry-in and carry-out value of one and no overflow.

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