The binary number 10111 is equivalent to the decimal number

A. 19

B. 31

C. 23

D. 22

To convert the binary number 10111 into its decimal equivalent, we need to understand how binary numbers work. Each digit in a binary number represents a power of 2, starting from the rightmost digit, which is 2^0. Let's break it down step by step.

Understanding Binary to Decimal Conversion

In the binary system, each digit can only be a 0 or a 1. The binary number 10111 can be analyzed as follows:

• The rightmost digit (1) is in the 2^0 place.
• The next digit (1) is in the 2^1 place.
• The next digit (1) 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.

Calculating Each Place Value

Now, let's assign the powers of 2 to each digit:

• 1 × 2^4 = 1 × 16 = 16
• 0 × 2^3 = 0 × 8 = 0
• 1 × 2^2 = 1 × 4 = 4
• 1 × 2^1 = 1 × 2 = 2
• 1 × 2^0 = 1 × 1 = 1

Adding the Values Together

Now, we simply add these values together:

• 16 + 0 + 4 + 2 + 1 = 23

Thus, the binary number 10111 is equivalent to the decimal number 23. Therefore, the correct answer is C. 23.

Why This Matters

Understanding binary to decimal conversion is crucial in computer science and digital electronics, as computers operate using binary numbers. This knowledge helps in grasping how data is processed and stored in digital systems.