‘The binary number 10101 is equivalent to decimal number Select one: a. 19 b. 21 c; 27 d. 12’
The correct answer and explanation is:
Correct Answer: b. 21
Explanation (300 words):
Binary numbers are a base-2 numeral system, meaning they use only two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is 202^0).
Let’s break down the binary number 10101:
We label each digit with its corresponding power of 2 position:
Binary: 1 0 1 0 1
Position: 4 3 2 1 0 (right to left)
Power of 2: 2⁴ 2³ 2² 2¹ 2⁰
Now, multiply each digit by its corresponding power of 2:
- 1×24=1×16=161 \times 2^4 = 1 \times 16 = 16
- 0×23=0×8=00 \times 2^3 = 0 \times 8 = 0
- 1×22=1×4=41 \times 2^2 = 1 \times 4 = 4
- 0×21=0×2=00 \times 2^1 = 0 \times 2 = 0
- 1×20=1×1=11 \times 2^0 = 1 \times 1 = 1
Add up the results: 16+0+4+0+1=2116 + 0 + 4 + 0 + 1 = \boxed{21}
So, the binary number 10101 is equivalent to the decimal number 21.
Why This Matters:
Understanding how to convert binary to decimal is essential in computer science and digital electronics because computers operate using binary logic. Every number, letter, or instruction a computer processes is ultimately translated into binary. Learning to convert between binary and decimal helps build a foundation for more advanced concepts like programming, data encoding, and computer architecture.
This kind of problem also enhances logical thinking and numeracy, especially in contexts where low-level computation is relevant—like network protocols, memory addressing, or hardware design.
So, 10101₂ = 21₁₀, and the correct answer is (b) 21.