Let's solve the problem step by step: ## 1. **Understanding the Problem** - **DAC Type:** 16-bit, BCD input - **Full Scale Output:** 9.99 V - **Input Code:** 0110 1001 0101 0111 - **Find:** - Percentage resolution - Output voltage (\( V_o \)) for the given input code --- ## 2. **Resolution Calculation** ### **Step 1: Number of Possible Output Steps** - **BCD:** Each digit is represented by 4 bits. - **16 bits → 4 BCD digits.** - **Each digit: 0–9 → Total possible codes = 10,000** (0000 to 9999 in decimal). ### **Step 2: Resolution** - **Resolution = Smallest change in output voltage** - Number of steps = \( 10,000 \) (from 0000 to 9999) - Resolution (\( \Delta V \)): \[ \Delta V = \frac{\text{Full-scale output}}{\text{Number of steps} - 1} = \frac{9.99\,V}{9999} \] \[ \Delta V = 0.000999\,V = 0.999\,\text{mV} \] ### **Step 3: Percentage Resolution** \[ \text{Percentage Resolution} = \frac{\text{Resolution}}{\text{Full-scale output}} \times 100\% \] \[ \text{Percentage Resolution} = \frac{0.000999}{9.99} \times 100\% \approx 0.01\% \] --- ## 3. **Output Voltage for the Given Input Code** ### **Step 1: Convert BCD Input to Decimal** Given code: **0110 1001 0101 0111** Group into 4 bits (from left): - 0110 = 6 - 1001 = 9 - 0101 = 5 - 0111 = 7 So, **Input Decimal Value = 6957** ### **Step 2: Output Voltage Calculation** \[ V_o = \frac{\text{Input Decimal Value}}{\text{Maximum Input Value}} \times \text{Full-scale output} \] - Maximum Input Value = 9999 \[ V_o = \frac{6957}{9999} \times 9.99 \] \[ V_o = 0.695769 \times 9.99 \approx 6.944\,V \] --- ## 4. **Final Answers** ### **(a) Percentage resolution:** \[ \boxed{0.01\%} \] ### **(b) Output voltage for input 0110~1001~0101~0111:** \[ \boxed{6.94\,V} \] (Rounded to 2 decimal places) --- ## **Summary Table** | Quantity | Value | |-------------------------|-----------------| | Percentage Resolution | 0.01% | | Output Voltage (\(V_o\))| 6.94 V |