How many distinct minterms exist in the complete sum-of-minterms expansion for a Boolean function of four variables?

How many distinct minterms exist in the complete sum-of-minterms expansion for a Boolean function of four variables?

• A. 16
• B. 8
• C. 4
• D. 32

Answer: (A)

In a Boolean function with n variables, a minterm is a product term that corresponds to one exact input combination of all the variables. There are 2^n possible input patterns, so there are 2^n distinct minterms. For four variables, that is 2^4 = 16 minterms. The complete sum-of-minterms form writes the function as the OR of the minterms for exactly those input patterns that yield 1. So the universe of possible distinct minterms is 16, though a specific function may use fewer of them depending on where it outputs 1.

In a Boolean function with n variables, a minterm is a product term that corresponds to one exact input combination of all the variables. There are 2^n possible input patterns, so there are 2^n distinct minterms. For four variables, that is 2^4 = 16 minterms. The complete sum-of-minterms form writes the function as the OR of the minterms for exactly those input patterns that yield 1. So the universe of possible distinct minterms is 16, though a specific function may use fewer of them depending on where it outputs 1.