Digital Electronics And Logic Gates

Step 1: Understanding the MOD counter.
The number of flip-flops required for a MOD-N counter is given by the formula: For MOD-31, we need to find such that .

Step 2: Calculate the number of flip-flops.
Since and , the smallest for which is . Thus, the number of flip-flops required for MOD-31 is 5.
Final Answer:

Step 1: Understanding the Johnson counter.
In an 8-bit Johnson counter, the output frequency is half of the input frequency.

Step 2: Calculate the output frequency.
Given the input frequency of 256 GHz, the output frequency will be:
Final Answer:

Step 1: Understanding the maxterms. A maxterm corresponds to the OR of all variables, where each variable is complemented if its value is 0 in the truth table. For the function , the corresponding maxterms are:
Final Answer:

Step 1: Understanding the characteristic equations.
The characteristic equation for flip-flops varies depending on the type of flip-flop.
For an SR flip-flop, the equation is , which matches with (A).
For a JK flip-flop, the equation is , which matches with (C).

Step 2: Conclusion. Thus, the correct answer is (A) and (C) only.
Final Answer:

Concept:
A MOD-N counter is a digital counter that cycles through N distinct states before repeating the sequence. The number of flip-flops required depends on the number of states that must be represented.
Step 1:Determining the number of flip-flops.
The number of flip-flops required is determined by the smallest integer satisfying: where is the modulus of the counter.
Step 2:Applying the formula for MOD-31.
For a MOD-31 counter: Thus, 5 flip-flops are required to represent at least 31 states.
Step 3:Type of counter implementation.
A commonly used implementation for such counters is the asynchronous (ripple) counter, where flip-flops toggle sequentially based on the output of the previous stage. Conclusion:
Therefore, a MOD-31 counter requires 5 flip-flops, and it is typically implemented using an asynchronous (ripple) counter.