If `(101)_2 + (1100)_2 div (10)_2 = (z)_10` , then what is the value of `z` ?

Options

A. 8
B. 9
C. 10
D. 11

Answer

To solve the equation `(101)_2 + (1100)_2 ÷ (10)_2 = (z)_10`, we will follow these steps:

### Step 1: Convert Binary Numbers to Decimal
1. **Convert `(101)_2` to decimal:**
- The binary number `(101)_2` can be calculated as follows:
\[ 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 1 \times 4 + 0 \times 2 + 1 \times 1 = 4 + 0 + 1 = 5 \]
So, `(101)_2 = 5_{10}`.

2. **Convert `(1100)_2` to decimal:**
- The binary number `(1100)_2` can be calculated as follows:
\[ 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 1 \times 8 + 1 \times 4 + 0 \times 2 + 0 \times 1 = 8 + 4 + 0 + 0 = 12 \]
So, `(1100)_2 = 12_{10}`.

3. **Convert `(10)_2` to decimal:**
- The binary number `(10)_2` can be calculated as follows:
\[ 1 \times 2^1 + 0 \times 2^0 = 1 \times 2 + 0 \times 1 = 2 + 0 = 2 \]
So, `(10)_2 = 2_{10}`.

### Step 2: Substitute Decimal Values into the Equation
Now substitute the decimal values we found into the equation:
\[ 5 + 12 \div 2 = z \]

### Step 3: Perform Division
Next, we perform the division:
\[ 12 \div 2 = 6 \]

### Step 4: Perform Addition
Now, substitute the result back into the equation:
\[ 5 + 6 = z \]

### Step 5: Calculate the Final Value of z
Finally, calculate the value of \( z \):
\[ z = 11 \]

Thus, the value of \( z \) is \( 11 \).

### Summary
The final answer is:
\[ z = 11 \]