How many Flip flop are required for sequence detector to detect 111011 sequence

1. Break Down the Problem

To determine the number of flip-flops required for a sequence detector that detects the sequence "111011", we need to follow these steps:

• Identify the sequence to be detected.
• Analyze the states required for the detection of the entire sequence.
• Calculate the minimum number of flip-flops needed.

2. Relevant Concepts

A sequence detector typically works with states corresponding to each part of the sequence that is matched. The total number of states can be determined by the length of the sequence and the need for a reset state.

3. Analysis and Detail

The sequence "111011" has a total of 6 bits. To create a state diagram for this sequence:

1. Count the states for each bit correctly matched in sequence.
2. Each unique state corresponds to a flip-flop.

Assuming we include an additional state to handle transitions and reset, we can represent the states as follows:

• State 0: Start (no bits matched)
• State 1: 1 matched
• State 2: 11 matched
• State 3: 111 matched
• State 4: 1110 matched
• State 5: 11101 matched
• State 6: 111011 matched (final state to indicate detection)
• State 7: Reset state (when the sequence doesn't match)

This gives us a total of 7 states.

Now, to determine the number of flip-flops required: The number of flip-flops $n$ needed can be calculated using the formula:

$n \geq \lceil \log_2{(number \: of \: states)} \rceil$

Here, we have $number \: of \: states = 7$:

$n \geq \lceil \log_2{7} \rceil = \lceil 2.807 \rceil = 3$

4. Verify and Summarize

We have calculated that at least 3 flip-flops are needed to represent the 7 states necessary to detect the sequence "111011". Each flip-flop can store a binary bit, and together they can represent up to $2^3 = 8$ states, which is sufficient for our requirements.

Final Answer

A minimum of 3 flip-flops are required for the sequence detector to detect the sequence "111011".