What is the value of (10101)2 in the decimal number system?
2025
What is the value of (10101)2 in the decimal number system?
Answer: B. 21 — In the binary (base-2) positional number system, each digit's place value is a power of 2, increasing from right to left starting at 20. A binary number is…
- A.
42
- B.
21
- C.
22
- D.
20
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Correct answer: B
In the binary (base-2) positional number system, each digit's place value is a power of 2, increasing from right to left starting at 20. A binary number is converted to decimal by multiplying each digit by its place value and summing the results.
Write out the place values for a 5-digit binary number, from right to left: 24, 23, 22, 21, 20 — that is 16, 8, 4, 2, 1.
Align the digits of 10101 with these place values: 1 with 16, 0 with 8, 1 with 4, 0 with 2, 1 with 1.
Keep only the place values where the digit is 1: 16, 4, and 1.
Add the kept place values: 16 + 4 + 1 = 21.
Reverse-check by converting 21 back to binary via repeated division by 2: 21÷2=10 r1, 10÷2=5 r0, 5÷2=2 r1, 2÷2=1 r0, 1÷2=0 r1 — reading the remainders bottom-to-top gives 10101, confirming the conversion.