Commutative law can be represented using logic gates as follows:

According to the Associative law of multiplication, when ANDing two or more variables, the order in which the variables are arranged makes no difference. This law can be illustrated using AND gates as shown below:

According to this law, ORing two or more variables followed by ANDing the outcome with a single variable is equal to ANDing the single variable with each one of the two variables followed by ORing the products. This law also illustrates the process of factorization as shown below:

DeMorgan proposed two theories that are useful part of Boolean algebra. In practice, DeMorgans theorems gives mathematical confirmation of the equivalence of NAND and the negative OR gates and the equivalence of the NOR and the negative AND gates. One of the DeMorgans theories is stated as follows: The complement of the product of any two variables is equivalent to the sum of the complements of the two variables.

A four-variable Karnaugh map consists of sixteen cells, as shown in the figure below. The binary digits A and B are at the left side while the values C and D are across the top. The value of any given cell is binary values of A and B combined with the values of C and D. For instance, the cell in the upper ...