Find the logic equation for the truth table given:

A	B	Y
0	0	0
0	1	1
1	0	0
1	1	1

Correct option is D

1. Identity behavior: When a truth table shows Y identical to B across all rows, the logic equation is simply Y = B.
2. Independence from A: If outputs do not change with A, A is a don’t-care input for the function.
3. Simplification check: Use basic identities—$$\bar{B}B=0, X+\bar{X}=1$$​, and factoring—to test alternatives quickly.
4. Design implication: Implementing Y = B needs just a wire (or buffer), minimizing gates, delay and power.
5. Verification tip: Compare column-by-column: if two columns match exactly, they are logically equivalent.
6. Robustness: Expressions that simplify to constants (0/1) cannot fit a non-constant truth table; eliminate them first.

Knowledge Booster

• Why (a) is wrong: $$\bar{A}B(A+\bar{B}) = \bar{A}B\cdot A + \bar{A}B\cdot\bar{B} = 0 + 0 = 0$$​; contradicts rows where B = 1 but Y = 1.
• Why (b) is wrong: $$\bar{A}\bar{B}+A\bar{B} = \bar{B}(\bar{A}+A) = \bar{B}$$​; this outputs 1 when B = 0, the opposite of Y = B.
• Why (c) is wrong: $$(\bar{A}\bar{B})B = \bar{A}(\bar{B}B) = 0$$​, a constant zero function.
• Extra tip: If the truth table equals B, alternative equivalent forms include $$Y=(A+\bar{A})B=B$$​ and $$Y=B\cdot 1$$​; both reaffirm the identity.