Bit capacity question — maximum value with a fixed width: What is the largest unsigned decimal value representable using exactly six binary bits (no sign)?

Introduction / Context:
Determining the representable range for a given bit width is critical when specifying counters, timers, and address fields. For unsigned binary values, the maximum is governed directly by powers of two.

Given Data / Assumptions:

• Unsigned representation (no sign bit).
• Bit width: 6 bits.
• We seek the largest representable value.

Concept / Approach:
An unsigned n-bit binary field ranges from 0 to 2^n - 1. For n=6, that is 0 to 64 - 1 = 63. This corresponds to a bit pattern of six ones: 111111₂.

Step-by-Step Solution:
Compute 2^6 = 64.Subtract 1 → 64 - 1 = 63.Hence, the maximum unsigned value in 6 bits is 63.

Verification / Alternative check:
Binary 111111₂ equals 32 + 16 + 8 + 4 + 2 + 1 = 63; this confirms the formula and the value.

Why Other Options Are Wrong:
64 would require seven distinct values above zero (0 to 64 needs 7 bits because it includes 64).
127 and 128 correspond to maxima for 7 and 8 bits, not 6 bits.

Common Pitfalls:
Forgetting the “minus 1” when computing the maximum; accidentally using signed ranges which would be -32 to +31 for 6-bit two’s-complement.

Final Answer:
63