Evaluate the power of two: what is the decimal value of 2^3 (two raised to the third power)?

Introduction / Context:
Powers of two are the backbone of binary arithmetic, memory sizing, addressing, and timing divisions. Quickly converting between exponents and decimal values is a vital skill in digital design and computer engineering.

Given Data / Assumptions:

• We are asked for 2^3.
• All arithmetic is in base-10 output for clarity.
• No units or scaling factors are present.

Concept / Approach:
Exponentiation with an integer exponent n means repeated multiplication by the base: a^n = a * a * ... * a (n times). For base 2, small exponents are frequently memorized: 2^0 = 1, 2^1 = 2, 2^2 = 4, and 2^3 = 8, continuing as 16, 32, 64, etc.

Step-by-Step Solution:
Compute 2^3 = 2 * 2 * 2.First multiplication: 2 * 2 = 4.Second multiplication: 4 * 2 = 8.Therefore, the decimal value of 2^3 is 8.

Verification / Alternative check:
Consider binary counting: after 1, 10, and 11, the fourth unique value is 100(2), which equals 4 in decimal; adding another doubling to reach 1000(2) confirms 2^3 = 8.

Why Other Options Are Wrong:

• 2 and 4 correspond to 2^1 and 2^2, not 2^3.
• 6 is not a pure power of two; it is 2 * 3 not arising from exponentiation by an integer.

Common Pitfalls:

• Mistaking multiplication count (e.g., doing only two multiplications for 2^3).
• Confusing doubling sequences with addition; exponentiation grows much faster than linear addition.

Final Answer:
8