The minimum number of D flip-flops needed to design a mod-258 counter ...
Minimum number of D flip-flops needed to design a mod-258 counter
To design a mod-258 counter, we need to have a counter that can count from 0 to 257 (since it is a mod counter). The minimum number of D flip-flops required is determined by the number of bits needed to represent the maximum count value.
Binary representation of 257
To determine the number of bits required to represent 257, we convert it into binary form:
257 = 2^8 + 1 = 100000001 (9 bits)
Explanation
A D flip-flop is a sequential circuit that can store one bit of data. It has two inputs - a data input (D) and a clock input (CLK), and one output (Q). When the clock input transitions from low to high (rising edge), the output takes the value of the data input.
In a counter, each flip-flop represents one bit of the count value. The output of each flip-flop is connected to the data input of the next flip-flop in the sequence, and the clock input is connected to a clock signal.
Since we need to count up to 257, we need a counter with 9 bits. Each bit represents a power of 2. The least significant bit represents 2^0, the next bit represents 2^1, and so on.
Number of flip-flops
To represent a 9-bit count value, we need 9 D flip-flops. Each flip-flop represents one bit of the count value.
Therefore, the minimum number of D flip-flops needed to design a mod-258 counter is 9 (option A).
Conclusion
In summary, the minimum number of D flip-flops required to design a mod-258 counter is 9. This is determined by the number of bits needed to represent the maximum count value, which in this case is 257. Each flip-flop represents one bit of the count value, and therefore, 9 flip-flops are required to accommodate the 9-bit count value.