Consider the logic circuit given below: ImageQ = ?
2014
Consider the logic circuit given below:
ImageQ = ?
- A.
A'C + BC ' + CD
- B.
ABC + C'D
- C.
AB + BC' + BD'
- D.
AB' + AC' + C'D
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Correct answer: C
The circuit consists entirely of NAND gates. We analyze the output step-by-step from left to right.
1. Top-left NAND gate: Inputs are D and C. Output = (CD)'. This signal feeds into the second stage.
2. Middle NAND gate: Inputs are the output from step 1, (CD)', and input B. Output = ((CD)' · B)'. Applying De Morgan's Law: (CD)'' + B' = CD + B'.
3. Bottom-left NAND gate: Inputs are A and B. Output = (AB)'. This signal feeds into the final stage.
4. Final NAND gate: Inputs are the outputs from steps 2 and 3, which are (CD + B') and (AB)'. Output Q = ((CD + B') · (AB)')'.
5. Simplify Q: Apply De Morgan's Law to the final expression.
Q = (CD + B')' + ((AB)')'
Q = (CD)' · (B')' + AB
Q = (C' + D') · B + AB
Q = BC' + BD' + AB
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