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The addition of two binary variables A and B results in a SUM and a CARRY output. Consider the following expressions for SUM and CARRY outputs. (a) SUM \( = A \cdot B + \;\overline {AB} \) (b) SUM = A⋅B̅ + A̅ ⋅ B (c) CARRY = A⋅B (d) CARRY = A + B Which of the following expressions are correct?

The addition of two binary variables A and B results in a SUM and a CARRY output. Consider the following expressions for SUM and CARRY outputs. (a) SUM \( = A \cdot B + \;\overline {AB} \) (b) SUM = A⋅B̅ + A̅ ⋅ B (c) CARRY = A⋅B (d) CARRY = A + B Which of the following expressions are correct? Correct Answer (b) and (c)

Concept:

In binary arithmetic:

  • 0 + 0 = 0 (No carry)
  • 0 + 1 = 1 (No carry)
  • 1 + 0 = 1 (No carry)
  • 1 + 1 = 0 (Carry = 1)


It’s corresponding truth table is drawn below:

A

B

Sum

Carry

0

0

0

0

0

1

1

0

1

0

1

0

1

1

0

1

Using K-map for the above truth table, we can get the expression for sum & carry. This is as shown:

[ alt="F1 S.B Deepak 28.02.2020 D9" src="//storage.googleapis.com/tb-img/production/20/03/F1_S.B_Deepak_28.02.2020_D9.png" style="width: 285px; height: 159px;">

Sum = A B̅ + A̅ B & Carry = AB

Hence Option (2) is correct.

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