For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct? 

For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct?  Correct Answer 1 only

Half-subtractor:

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The Truth Table for a half subtractor is drawn as:

The Boolean expression for difference can be written as:

N = A̅ B + A B̅ 

N = A ⊕ B

And the Boolean expression for the borrow can be written as:

M = A̅ B

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half adder:

A half adder circuit is basically made up of and a AND gate with XOR gate as shown below.

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• A half adder is also known as XOR gate because XOR is applied to both inputs to produce the sum
• Half adder can add only two bits (A and B) and has nothing to do with the carry
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits
• That means the binary addition process is not complete and that's why it is called a half adder

Sum (S) = A⊕B, Carry = A.B