QB_PH_SEC8_025: Digital Electronics

Which of the following logic gates is classified as a 'Universal Gate' capable of synthesizing any arbitrary Boolean function without other gate types?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Universal Gate Definition**: A logic gate is functionally complete (universal) if any Boolean logic expression can be implemented using exclusively that gate type. 2. **NAND Syntheses**: - **NOT**: Connect both inputs together: $\overline{A \cdot A} = \bar{A}$ - **AND**: Invert a NAND output: $\overline{\overline{A \cdot B}} = A \cdot B$ - **OR**: By De Morgan's theorem: $A + B = \overline{\bar{A} \cdot \bar{B}}$ (NAND of inverted inputs) 3. **Conclusion**: NAND gate is universal. Option (A) is correct.