Chapter 07 - Multilevel Logic-2x2(1)

# Although each function could be realized separately

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: based on DeMorgan′s Laws Figure 7-14: Alternative Gate Symbols Figure 7-16: Conversion to NOR Gates Figure 7-15: NAND Gate Circuit Conversion Design of Two-Level, Multiple-Output Circuits Solution of digital design problems often requires the realization of several functions of the same variables. Although each function could be realized separately, the use of some gates in common between two or more functions sometimes leads to a more economical realization. Example: Figure 7-17: Conversion of AND-OR Circuit to NAND Gates Design a circuit with four inputs and three outputs which realizes the functions F1(A, B, C, D) = Ʃ m(11, 12, 13, 14, 15) F2(A, B, C, D) = Ʃ m(3, 7, 11, 12, 13, 15) F3(A, B, C, D) = Ʃ m(3, 7, 12, 13, 14, 15) (7-22) Section 7.6 (p. 204) Realization of functions separately (9 Gates) F1(A, B, C, D) = Ʃ m(11, 12, 13, 14, 15) F2(A, B, C, D) = Ʃ m(3, 7, 11, 12, 13, 15) F3(A, B, C, D) = Ʃ m(3, 7, 12, 13, 14, 15) Figure 7-19: Realization of Equations (7-22) Another example of sharing gates among multiple outputs to reduce cost. f1 = Ʃ m(2, 3, 5, 7, 8, 9, 10, 11, 13, 15) f2 = Ʃ m(2, 3, 5, 6, 7, 10, 11, 14, 15) f3 = Ʃ m(6, 7, 8, 9, 13, 14, 15) Realization of functions with shared gates (lower overall cost) (7 Gates) Figure 7-21 Multiple-Output Realization of Eqns (7-22) Minimal Solution In this example, the best solution is obtained by not combining the circled 1 with adjacent 1’s. f1 = a′bd + abd + ab′c′ + b′c f2 = c + a′bd f3 = bc + ab′c′ + abd Figure 7-22 The procedure for design of single-output, multi-level NAND- and NOR-gate circuits also applies to multiple-output circuits The solution with the maximum number of common terms is not necessarily the best solution, as illustrated by this example. Figure 7-23...
View Full Document

## This document was uploaded on 03/16/2014 for the course EE 316 at University of Texas at Austin.

Ask a homework question - tutors are online