Digital Electronics Lecture 6 Combinational Logic Circuit Design

Lecture 6 outline Review of last Lecture Design procedure for simple combinational logic circuits Continuation of Simulation exercises

Review of Last Lecture Simplification using K-map Simplification using logic converter in Multisim

DESIGN PROCEDURE FOR SIMPLE COMBINATIONAL LOGIC CIRCUIT 1- Write out the truth table for the required function. 2- From the truth table, write down the Boolean equation for the output. 3- Minimize the equation if appropriate. (using Karnough map). 4- Apply DeMorgan theorem as appropriate. 5- Draw out the circuit using NAND (or NOR) gates. Apply rules 4 and 5 if the circuit is restricted to one type of gates only.

Example 1 Design a NAND gate Implementation of the following truth table. ABC F Starting Point

Using Boolean Algebra 2- F = A _ BC + AB _ C + ABC _ +ABC 3- Adding redundant term ABC many times. F = BC (A _ + A) + AC(B _ +B) + AB (C _ +C) F = BC + AC + AB 4- Apply DeMorgan theorem F = BC. AC. AB

Example 2 This circuit is one of many employed in the arithmetic logic unit of a digital computer. It basically generates a Sum and a Carry simultaneously whilst adding a pair of one bit numbers. ABSumCarry Sum = A _ B + AB _ Carry = A.B

FULL ADDER

Truth table ABCinSumCarry

S = A _ B _ C + A _ BC _ +AB _ C _ + ABC S = C (A _ B _ +AB) + C _ ( A _ B + AB _ ) S = C (A+B) + C _ ( A + B) S = A + B + C Co = A _ BC + AB _ C + ABC _ + ABC Co = C ( A _ B + AB _ ) + AB C = C(A + B) + AB

MULTIPLEXER A multiplexer (MUX) is a device that allows digital information from several sources to be routed onto a single line for transmission over the line to a common destination.

Data Select InputsInput Selected S1S S _ 1 S _ 0 AA 01S _ 1 S0 BB 10S1 S _ 0 CC 11S1 S0 DD X = S _ 1 S _ 0 A + S _ 1 S0 B + S1 S _ 0 C + S1 S0 D

Main Points Design procedure for combinational logic circuits. Adders Multiplexer Simulation exercises using logic converter

The End Thank you for your attention.