Largest decimal value in a 4-bit binary counter: What is the decimal equivalent of the maximum binary number representable with 4 bits?

Introduction / Context:Binary counters use a certain number of flip-flops to represent states. With 4 bits, the representable unsigned values range from 0 to 2^4 - 1. Knowing the maximum value helps determine range, modulus, and overflow behavior in digital designs.

Given Data / Assumptions:

• We consider an unsigned 4-bit binary number.
• Binary range formula: 0 through 2^N - 1 for N bits.
• No sign bit or special encoding is assumed.

Concept / Approach:For N bits, the highest unsigned value is 2^N - 1. Substituting N = 4 gives 2^4 - 1 = 16 - 1 = 15. In binary, this is 1111. Many counters therefore have a modulus of 16 when all 4-bit states are used.

Step-by-Step Solution:

Verification / Alternative check:List the 4-bit codes from 0000 to 1111 and sum the weights of 1111 to verify 15. Simulation or a counter datasheet (MOD-16) corroborates this.

Why Other Options Are Wrong:

Common Pitfalls:Off-by-one errors when applying 2^N; confusing the count of states (16) with the largest numeric value (15).

Final Answer:15