QB_PH_SEC8_022: Digital Electronics

A digital half-adder circuit takes two binary inputs $A = 1$ and $B = 1$. What are the values of the Sum ($S$) and Carry ($C$) outputs respectively? (Enter your answer as a 2-digit number $SC$, e.g., if $S=1, C=0$, enter 10)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Boolean Equations for Half Adder**: - Sum bit: $S = A \oplus B = A\bar{B} + \bar{A}B$ - Carry bit: $C = A \cdot B$ 2. **Evaluation for $A = 1, B = 1$**: $S = 1 \oplus 1 = 0$ $C = 1 \cdot 1 = 1$ 3. **Arithmetic Interpretation**: $1_2 + 1_2 = 10_2$ (decimal 2), where the higher place value is Carry ($1$) and lower bit is Sum ($0$). 4. **Format $SC$**: $S = 0, C = 1 \implies 01$ (or value 1).