Derive Logic Equation from Karnaugh Map of RS Flip Flop

[iamnew]

Homework Statement

I have attached a jpeg image of a karnough map of a rs flip flop. How can i derive the logic equation?

Homework Equations

The Attempt at a Solution

 

[berkeman]

Homework Statement

I have attached a jpeg image of a karnough map of a rs flip flop. How can i derive the logic equation?

Homework Equations

The Attempt at a Solution

What is "out"? It looks like you have the previous "q" on the left, and then the next output "Q" is what is in the truth table, no?

 

[Mene]

To derive the logic equation from a Karnaugh map of a RS flip flop, we first need to understand the Karnaugh map and its purpose. A Karnaugh map is a graphical representation of a truth table, where the input and output values are represented by squares instead of binary digits. This allows for easier simplification of logic expressions.

In order to derive the logic equation, we need to follow these steps:

1. Identify the input variables: In the Karnaugh map provided, we can see that there are two input variables - R (reset) and S (set).

2. Group the squares: We need to group the adjacent squares that have a value of 1. These groups should be of size 2^n, where n is a positive integer. In this case, we can see that there are two groups of size 2 - one in the top left corner and one in the bottom right corner.

3. Determine the output values for each group: The output value for each group is determined by the value of the flip flop after the input values have been applied. In this case, we can see that the output values for the two groups are Q (output) = 0 and Q = 1.

4. Write the logic expression for each group: Based on the output values, we can write the logic expression for each group. For the group with Q = 0, the logic expression would be Q = R'. For the group with Q = 1, the logic expression would be Q = S.

5. Combine the logic expressions: Finally, we can combine the logic expressions for each group using the OR operator. This gives us the final logic equation for the RS flip flop:

Q = (R' + S)

In conclusion, by following these steps, we can derive the logic equation for a RS flip flop from its Karnaugh map representation. This equation can then be used to design and analyze RS flip flop circuits in different applications.