Understanding the 4-Bit Counter

A 4-bit counter is a type of digital circuit specifically designed to count in a sequence using four binary digits (bits). Each individual bit can only represent two possible values: either 0 or 1.

Calculating Total Possible States

To determine the range of numbers a counter can represent, we calculate the total number of unique states it can achieve. With 'k' bits, the total number of states is calculated using the formula $2^k$.

In this specific case, the counter is a 4-bit counter, meaning $k=4$. The calculation proceeds as follows:

• Total States = $2^4$
• $2^4 = 2 \times 2 \times 2 \times 2 = 16$

This calculation shows that a 4-bit counter is capable of representing exactly 16 distinct values or states.

Determining the Maximum Count Value 'n'

Digital counters typically commence their counting sequence from the value 0. The sequence then progresses through consecutive integer values until it reaches the highest possible value representable by the number of bits. This maximum value is represented as 'n' in the question.

The complete counting sequence includes the starting value (0) and all subsequent values up to the maximum value 'n'. Therefore, the total number of values counted is always one more than the maximum value. This can be expressed as:

• Total Values = $n + 1$

We have already established that a 4-bit counter has a total of 16 possible states (values). We can use this information to set up an equation:

• $16 = n + 1$

To find the specific value of 'n', we need to solve this simple algebraic equation:

• $n = 16 - 1$
• $n = 15$

This result means that the counting sequence for a 4-bit counter runs from 0 up to 15.

Conclusion on Value 'n'

Based on the calculation, the maximum value 'n' that a 4-bit counter reaches when counting sequentially starting from 0 is 15.