Question

The decimal equivalent of \( 10010_{(2)} \) is:

• A. \(16_{(10)}\)
• B. \(21_{(10)}\)
• C. \(18_{(10)}\)
• D. \(24_{(10)}\)

Hint:

Remember the place values in binary are powers of 2, starting from \(2^0\) on the rightmost digit.

Answer 1

The Correct Option is C

Step 1: Understand Binary Number System.
The binary number system is a base-2 system, using only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from \(2^0\) on the rightmost digit and increasing by one power of 2 as you move to the left. Step 2: Identify the place value of each digit in \(10010_{(2)\).}
From right to left, the place values are:
The rightmost digit (0) is in the \(2^0\) place.
The next digit (1) is in the \(2^1\) place.
The next digit (0) is in the \(2^2\) place.
The next digit (0) is in the \(2^3\) place.
The leftmost digit (1) is in the \(2^4\) place.
Step 3: Multiply each binary digit by its corresponding place value.
\(1 \times 2^4 = 1 \times 16 = 16\)
\(0 \times 2^3 = 0 \times 8 = 0\)
\(0 \times 2^2 = 0 \times 4 = 0\)
\(1 \times 2^1 = 1 \times 2 = 2\)
\(0 \times 2^0 = 0 \times 1 = 0\)
Step 4: Sum the results from Step 3 to get the decimal equivalent. \(16 + 0 + 0 + 2 + 0 = 18\)
Therefore, the decimal equivalent of \(10010_{(2)}\) is \(18_{(10)}\).