Digital basics — the number of distinct values representable by an n-bit binary word is given by which expression?

Introduction / Context:Digital systems encode information using binary digits (bits). The count of unique binary patterns determines how many distinct states (numbers, codes) the system can represent. This question checks the fundamental relationship between bit width and representable combinations.

Given Data / Assumptions:

• Word length n is the number of bits.
• Each bit can be 0 or 1 (two possibilities).
• Bits are independent in the combinatorial sense.

Concept / Approach:For n independent binary places, the number of unique binary patterns is 2 * 2 * … (n times) = 2^n. This holds whether the word is used as unsigned magnitude, two’s complement, addresses, or arbitrary codes; the encoding may map patterns differently but the count of distinct patterns remains 2^n.

Step-by-Step Solution:

Verification / Alternative check:Examples: 1 bit → 2 combinations; 2 bits → 4; 8 bits → 256; 16 bits → 65,536. All equal 2^n.

Why Other Options Are Wrong:

• Analog word references are irrelevant; the question is digital combinatorics.
• Multiplying 2 by the number of bits yields 2n, not 2^n.
• “Determining range of the analog word” does not compute combinations.

Common Pitfalls:Confusing 2n with 2^n; mixing up representable values with numerical range conventions (e.g., signed vs unsigned).

Final Answer:Raising 2 to the number of bits in the digital word.