Power-of-two evaluation: what is the decimal value of 2^10 (two raised to the power 10)?

Introduction / Context:
Powers of two are central to digital systems because binary representation scales by factors of 2. Memorizing key powers (2^10, 2^20, etc.) accelerates mental math for storage capacities, addressing, and algorithm complexity. Here we evaluate 2^10 in decimal.

Given Data / Assumptions:

• Base = 2, exponent = 10.
• We want an exact decimal number.
• No approximations; exact integer evaluation.

Concept / Approach:
Use repeated doubling: each increment of the exponent multiplies the current value by 2. Alternatively, recall the common identity used in computing: 2^10 = 1024, which is close to 10^3 and often used for quick order-of-magnitude conversions between binary and decimal scales.

Step-by-Step Solution:

Verification / Alternative check:
Calculator or quick mental doubling confirms the result. Also, note that 1024 is widely used as a “binary thousand” in legacy contexts (though modern SI prefers 1000 while IEC uses 1024 = 1 kibibyte).

Why Other Options Are Wrong:

Common Pitfalls:
Mixing decimal and binary prefixes; remember that 2^10 = 1024 (1 Ki) while 10^3 = 1000 (1 k). In storage and networking, be attentive to whether SI (kilo) or IEC (kibi) units are used.

Final Answer:
1024