Digital number systems: The binary numeral system is based on powers of which base value?

Introduction / Context:Computers represent and process data using the binary numeral system. Understanding the base and place values of binary is foundational for logic design and programming.

Given Data / Assumptions:

• The system in question is the binary system.
• Place values scale by repeated powers of the base.

Concept / Approach:

In any positional numeral system, each digit position represents a power of the base. Decimal uses base 10 (10^0, 10^1, …). Binary uses base 2, so positions are 2^0, 2^1, 2^2, and so on.

Step-by-Step Solution:

Verification / Alternative check:

Example: 1011₂ = 12^3 + 02^2 + 12^1 + 12^0 = 8 + 0 + 2 + 1 = 11 in decimal.

Why Other Options Are Wrong:

• 10: base of decimal, not binary.
• 8: base of octal.
• 16: base of hexadecimal.
• None of the above: incorrect because 2 is correct.

Common Pitfalls:

• Confusing hexadecimal (base 16) used as a compact binary representation with the underlying binary base.

Final Answer:

2.