What is the value of X, if `(1010)_(2)xx (111)_(2) = (X)_(10)`?

Options

A. 60
B. 70
C. 75
D. 80

Answer

To solve the problem, we need to find the value of \( X \) in the equation \( (1010)_{2} \times (111)_{2} = (X)_{10} \).

### Step-by-Step Solution:

**Step 1: Convert the binary numbers to decimal.**

1. Convert \( (1010)_{2} \) to decimal:
- \( 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 \)
- \( = 1 \times 8 + 0 \times 4 + 1 \times 2 + 0 \times 1 \)
- \( = 8 + 0 + 2 + 0 = 10 \)

2. Convert \( (111)_{2} \) to decimal:
- \( 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 \)
- \( = 1 \times 4 + 1 \times 2 + 1 \times 1 \)
- \( = 4 + 2 + 1 = 7 \)

**Step 2: Multiply the decimal values.**

Now, we multiply the two decimal values obtained:
- \( 10 \times 7 = 70 \)

**Step 3: Write the result in decimal form.**

Thus, \( X = 70 \).

### Final Answer:
The value of \( X \) is \( 70 \).

---