The purpose of the Karnaugh map in a synchronous sequential circuit design is to pictorially identify all the possible conditions that will result in the flip-flop assuming a 1-state on the next clock pulse.

We take advantage of all non-existent states (since they don't exist and therefore don't matter) in order to simplify the boolean logic solution.

Karnaugh maps are also useful in preventing race problems. (This has nothing to do with racial tension in human society).

Here is the solution for the A flip-flop. (In this exercise, we assume that flip-flop A represents the least significant bit in the 4-bit BCD counter.)

We group all the 1s and Xs in the largest group possible, of eight's, four's or two's, remembering that the map wraps around an imaginary cylinder both horizontally and vertically.

It is ok to include the same square in more than one group.

In fact, when groups share a common square or squares, that is, when all groups overlap, this will ensure that race problems are eliminated.

In this example, the result is a single group of eight squares represented by the boolean A' (i.e. NOT A).

This result is intuitive for the least-significant bit A. That is, the A flip-flop toggles on every clock pulse.

We take advantage of all non-existent states (since they don't exist and therefore don't matter) in order to simplify the boolean logic solution.

Karnaugh maps are also useful in preventing race problems. (This has nothing to do with racial tension in human society).

Here is the solution for the A flip-flop. (In this exercise, we assume that flip-flop A represents the least significant bit in the 4-bit BCD counter.)

We group all the 1s and Xs in the largest group possible, of eight's, four's or two's, remembering that the map wraps around an imaginary cylinder both horizontally and vertically.

It is ok to include the same square in more than one group.

In fact, when groups share a common square or squares, that is, when all groups overlap, this will ensure that race problems are eliminated.

In this example, the result is a single group of eight squares represented by the boolean A' (i.e. NOT A).

This result is intuitive for the least-significant bit A. That is, the A flip-flop toggles on every clock pulse.

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