Convert the binary number 10110 (base 2) into its equivalent decimal (base 10) number.

Introduction / Context:
This question is about number system conversion from binary to decimal. Binary numbers use base 2 with digits 0 and 1. Each position represents a power of 2. We must convert the binary number 10110 into its base 10 (decimal) equivalent by expanding it in powers of 2.

Given Data / Assumptions:
The given binary number is 10110₂.We must express it as a decimal number.Binary positions from right to left represent 2^0, 2^1, 2^2, 2^3 and 2^4 respectively.

Concept / Approach:
To convert a binary number to decimal, multiply each binary digit by 2 raised to the power of its position index (starting from 0 at the rightmost digit) and then add all these products. Only positions with a 1 contribute to the sum; positions with a 0 contribute nothing.

Step-by-Step Solution:
Step 1: Write 10110 as digits with place values: 1 0 1 1 0.Step 2: Label the positions from right to left: the rightmost 0 is at 2^0, the next 1 is 2^1, then 1 at 2^2, 0 at 2^3 and 1 at 2^4.Step 3: Compute the contribution of each digit: 1 × 2^4 = 1 × 16 = 16; 0 × 2^3 = 0; 1 × 2^2 = 1 × 4 = 4; 1 × 2^1 = 1 × 2 = 2; 0 × 2^0 = 0.Step 4: Add these contributions: 16 + 0 + 4 + 2 + 0 = 22.Step 5: Therefore, 10110₂ equals 22₁₀ in decimal.

Verification / Alternative check:
We can also do the conversion using repeated doubling: starting from the left, process digits one by one. Begin with 1. Multiply by 2 and add the next digit: 1 × 2 + 0 = 2; then 2 × 2 + 1 = 5; 5 × 2 + 1 = 11; 11 × 2 + 0 = 22. This verifies that the decimal equivalent is 22.

Why Other Options Are Wrong:
The value 20 would correspond to a different binary number (e.g., 10100₂). The values 18 and 16 likewise correspond to other binary patterns. Only 22 matches the positional value calculation from 10110₂.

Common Pitfalls:
Common mistakes include assigning the wrong powers of 2 to each digit, especially mixing up the order, or forgetting to include one of the 1-digits in the sum. Carefully labeling each position with its correct power of 2 avoids these errors.

Final Answer:
The binary number 10110 corresponds to the decimal number 22.