Analytic expressions for the sizes of logically minimized truth tables for binary addition and subtraction.

Direct implementations of digital functions by truth table look-up techniques are of increasing importance in both optical and electronic processing. A major issue in these techniques is the logical minimization of the Boolean algebraic expressions for the functions being implemented. For most cases of practical interest, these minimizations require extensive computer time. In this paper, analytic expressions are derived that provide complete information about the absolute minimum sum-of-products representations for binary addition, with and without an input carry, and binary subtraction, with and without an input borrow. These expressions are applicable to any word length.