Binary word range — 6-bit maximum value: What is the largest unsigned integer value representable by a 6-bit binary word?

Introduction / Context:Bit width limits the numeric range of unsigned binary values. In general, an n-bit unsigned word represents integers from 0 to 2^n − 1. This is foundational for register sizing, counter design, and memory addressing.

Given Data / Assumptions:

• The word is 6 bits wide.
• Unsigned representation is assumed.
• We seek the maximum value.

Concept / Approach:For n bits, the count of distinct states is 2^n. The maximum unsigned integer is all bits set to 1. Therefore, with n = 6, max = 2^6 − 1.

Step-by-Step Solution:Compute 2^6 = 64.Subtract 1 to get the maximum: 64 − 1 = 63.Confirm binary: 111111₂ corresponds to decimal 63.

Verification / Alternative check:List endpoints: min = 0 (000000₂), max = 63 (111111₂) → 64 distinct values as expected.

Why Other Options Are Wrong:36 and 65 are not endpoints for 6 bits; 64 would require 7 bits for unsigned max.

Common Pitfalls:Confusing “number of states” (64) with “maximum value” (63).

Final Answer:63.