Final answer:
A minterm is a product of variables that equals 1 for a unique combination of input values, while a maxterm is a sum of variables that equals 0 for a specific input combination. Both are used in Boolean algebra to simplify expressions and design logic circuits.
Step-by-step explanation:
What are Minterm and Maxterm?
A minterm is an expression in Boolean algebra that represents a unique combination of variables in a truth table that results in the output being true (1). A minterm is a product (AND) of all the variables in the table, each of which can be in its true form or complemented (negated) form. For example, if we have two variables, A and B, one minterm could be A AND NOT B (AB'). This minterm corresponds to the condition where A=1 and B=0.
Conversely, a maxterm is a sum (OR) of all the variables in the truth table that yields the output false (0) for a particular combination of variables. Each variable in a maxterm is also in its true form or complemented form. If we use the same variables, A and B, one maxterm example is NOT A OR B (A'+B). This maxterm corresponds to the condition A=0 or B=1. Both minterms and maxterms are used in the simplification of Boolean expressions and play a crucial role in the design of digital systems, such as constructing truth tables and implementing logic circuits.