Power-of-two evaluation What decimal value does 2^5 represent?
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A10
-
B31
-
C25
-
D32
Answer
Correct Answer: 32
Explanation
Introduction / Context:Powers of two are fundamental in digital systems because binary place values are powers of 2. Evaluating 2^n is straightforward multiplication by 2 repeated n times.
Given Data / Assumptions:
- Base = 2.
- Exponent n = 5.
- 2^n means multiply 2 by itself n times.
Concept / Approach:Compute 2^5 using successive doubling or by recognizing that 2^5 is the next value after 2^4 = 16.
Step-by-Step Solution:
1) 2^1 = 2.2) 2^2 = 4.3) 2^3 = 8.4) 2^4 = 16.5) 2^5 = 32.Verification / Alternative check:Binary 100000 equals 32 decimal, which corresponds to 2^5.
Why Other Options Are Wrong:
- 10/31/25: Do not equal 2^5; 31 is one less than 32, and 25 confuses with the decimal digits 2 and 5.
Common Pitfalls:Reading “2^5” as the decimal number 25 instead of a power.
Final Answer:32