Question

what do you think: what does 11111 represent in decimal? choose 1 answer. a 15 b 24 c 31 d 63

Explanation:

Step1: Identify the base

Assume 11111 is a binary number (since it's a common binary-to-decimal conversion problem). In binary, each digit represents a power of 2, starting from the rightmost digit as \(2^0\).

Step2: Expand the binary number

For the binary number \(11111_2\), we can expand it as:
\[
1\times2^4 + 1\times2^3 + 1\times2^2 + 1\times2^1 + 1\times2^0
\]

Step3: Calculate each term

• \(2^4 = 16\), so \(1\times2^4 = 16\)
• \(2^3 = 8\), so \(1\times2^3 = 8\)
• \(2^2 = 4\), so \(1\times2^2 = 4\)
• \(2^1 = 2\), so \(1\times2^1 = 2\)
• \(2^0 = 1\), so \(1\times2^0 = 1\)

Step4: Sum the terms

Add all the calculated terms together:
\[
16 + 8 + 4 + 2 + 1 = 31
\]

Answer:

C. 31