S-R Flip-Flop Construction using NOR gates

To construct a basic S-R flip-flop, we can use a combination of NOR gates. The S-R flip-flop is a fundamental building block in digital circuits and is used to store a single bit of information. It has two inputs, S (set) and R (reset), and two outputs, Q and Q̅ (complement of Q).

Truth Table
The truth table of an S-R flip-flop is as follows:

S | R | Q | Q̅
--|---|---|---
0 | 0 | Q | Q̅
0 | 1 | 0 | 1
1 | 0 | 1 | 0
1 | 1 | - | -

Design using NOR gates
The cross-coupling of NOR gates allows us to implement an S-R flip-flop. Here is the construction using NOR gates:

1. Connect the S input to one input of a NOR gate and the R input to one input of another NOR gate.
2. Connect the Q output to one input of the NOR gate corresponding to the R input.
3. Connect the Q̅ output to one input of the NOR gate corresponding to the S input.
4. Connect the output of the NOR gate connected to the R input to the other input of the NOR gate connected to the S input.
5. Connect the output of the NOR gate connected to the S input to the other input of the NOR gate connected to the R input.

Explanation
When both S and R inputs are low (0), the NOR gates produce high outputs, maintaining the previous state of the flip-flop. This forms a stable state where Q and Q̅ remain unchanged.

When S is high (1) and R is low (0), the NOR gate connected to S input produces a low output, which is connected to the R input NOR gate. This results in a high output at Q and a low output at Q̅, setting the flip-flop to the state Q=1.

Similarly, when S is low (0) and R is high (1), the NOR gate connected to R input produces a low output, which is connected to the S input NOR gate. This results in a low output at Q and a high output at Q̅, resetting the flip-flop to the state Q=0.

Finally, when both S and R inputs are high (1), it creates a condition called the "forbidden" state, where the outputs of the NOR gates are unpredictable. Therefore, this state is avoided in practical designs.

Thus, the cross-coupling of NOR gates allows us to construct a basic S-R flip-flop that can store and manipulate a single bit of information.