The reference voltage is 11 V in a 3-bit binary weighted ladder D/A converter. The digital input is 101
binary. R1 is .
Using the formula for the step size/resolution of a binary ladder D/A converter and the formula Vo = (Din in
decimal) (step size).
What is Vo in volts?
Round your answer to 3 decimal places.
Vo

Ask by Cruz Weston. in the United States

Mar 20,2025

Question

The reference voltage is 11 V in a 3-bit binary weighted ladder D/A converter. The digital input is 101
binary. R1 is .
Using the formula for the step size/resolution of a binary ladder D/A converter and the formula Vo = (Din in
decimal) (step size).
What is Vo in volts?
Round your answer to 3 decimal places.
Vo

Ask by Cruz Weston. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

To find $$ V_o $$ for the given 3-bit binary weighted ladder D/A converter, we will follow these steps:

1. **Convert the binary input to decimal**: The binary input is $$ 101 $$.
2. **Calculate the step size**: The formula for the step size $$ S $$ in a binary weighted D/A converter is given by:
   $$
   S = \frac{V_{ref}}{2^n}
   $$
   where $$ V_{ref} $$ is the reference voltage and $$ n $$ is the number of bits.
3. **Calculate $$ V_o $$**: Using the formula:
   $$
   V_o = (D_{in} \text{ in decimal}) \times S
   $$

Now, let's perform the calculations step by step.

### Step 1: Convert binary to decimal
The binary number $$ 101 $$ in decimal is:
$$
D_{in} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5
$$

### Step 2: Calculate the step size
Given:
- $$ V_{ref} = 11 \, V $$
- $$ n = 3 $$

Now, we can calculate the step size $$ S $$:
$$
S = \frac{11}{2^3} = \frac{11}{8}
$$

### Step 3: Calculate $$ V_o $$
Now we can calculate $$ V_o $$:
$$
V_o = D_{in} \times S = 5 \times \frac{11}{8}
$$

Let's compute $$ V_o $$ and round it to 3 decimal places.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times \frac{11}{8}$$
- step1: Multiply:
  $$\frac{5\times 11}{8}$$
- step2: Multiply:
  $$\frac{55}{8}$$
The calculated value of $$ V_o $$ is $$ 6.875 $$ volts.

Thus, rounded to three decimal places, $$ V_o = 6.875 \, V $$.
$$ V_o = 6.875 $$ volts

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Solución

Step 1: Convert binary to decimal

Step 2: Calculate the step size

Step 3: Calculate

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