Optimal Two-Level Boolean Minimization

Years and Authors of Summarized Original Work

• 1952; Quine

• 1955; Quine

• 1956; McCluskey

Problem Definition

Find a minimal sum-of-products expression for a Boolean function. Consider a Boolean algebra with elements False and True. A Boolean function f(y₁, y₂, …, y _n ) of n Boolean input variables specifies, for each combination of input variable values, the function’s value. It is possible to represent the same function with various expressions. For example, the first and last expressions in Table 1 correspond to the same function. Assuming access to complemented input variables, straightforward implementations of these expressions would require two AND gates and an OR gate for $\left (\overline{a} \wedge \overline{b}\right ) \vee \left (\overline{a} \wedge b\right )$ and only a wire for $\overline{a}$. Although the implementation efficiency depends on target technology, in general terser expressions enable greater efficiency. Boolean minimization is the task of deriving the tersest...