Determine the decoded 12-bit code for a resolution of 0.01 V and analog sample voltages +10.234 V.Answer format: XXXXXXXXXXXX, where X is either 1 or 0.

1. Break Down the Problem

To determine the decoded 12-bit code for a given analog sample voltage, we need to perform the following steps:

1. Determine the maximum digital code based on the resolution.
2. Calculate the number of steps corresponding to the sample voltage.
3. Convert the number of steps to a 12-bit binary code.

2. Relevant Concepts

1. The resolution $R$ of the analog-to-digital converter (ADC) can be given by the formula: $R = \frac{V_{\text{max}} - V_{\text{min}}}{2^n}$ where $V_{\text{max}}$ and $V_{\text{min}}$ are the maximum and minimum input voltages, and $n$ is the number of bits (in this case, $n = 12$).

2. The digital code can be calculated using: $\text{Digital Code} = \frac{V_{\text{sample}} - V_{\text{min}}}{R}$

3. Analysis and Detail

1. Determine the Maximum Digital Code: If the ADC converts voltages from $0$ V to $+10$ V (assuming $V_{\text{min}} = 0$ and $V_{\text{max}} = +10$):

   • Since the resolution $R = 0.01$ V: $2^{12} = 4096 \quad \text{(maximum digital codes)}$

2. Calculate the Steps:

   • The formula for $R$: $R = \frac{V_{\text{max}} - V_{\text{min}}}{2^{12}} = \frac{10 - 0}{4096} = \frac{10}{4096} \approx 0.00244140625 \text{ V}$

3. Convert Sample Voltage to Digital Code:

   • For a sample voltage $V_{\text{sample}} = +10.234$ V: $\text{Digital Code} = \frac{V_{\text{sample}}}{R} = \frac{10.234}{0.00244140625} \approx 4191.428 \quad (\text{as digital code should be an integer, take } 4191)$

4. Convert to 12-Bit Binary:

   • $4191$ in binary is: $4191 = 100000110111$
   • Pad with zeros on the left to make it 12 bits: $4191 = 111111001111 \quad (\text{only the last 12 bits are relevant})$

4. Verify and Summarize

The calculated digital code for the sample voltage $+10.234$ V using a 12-bit ADC, with a resolution of $0.01$ V, is $111111001111$.

Final Answer

111111001111