Lecture 1: Introduction to Digital Logic Design CK Cheng Thursday 9/26/02

We will cover four major things in this course: - Combinational Logic - Sequential Networks - Standard Modules - System Design

Overall Picture of CS140 Mux Memory ALU Memory Control Subsystem conditions control input Pointer

Two Types of Circuits Combinational logic: fi(x) x1. xn y i = f i (x 1,..x n ) xi CLK Sequential Networks 1) Memory 2) Time Steps (Clock) y i t = f i (x 1 t,…x n t, s 1 t, … s n t ) S i t+1 = g i (x 1 t,…,x n t, s 1 t,….s n t )

Part I. Combinational Logic I) Specification II) Implementation III) Different Types of Gates ab + cd abab cdcd e cd ab e (ab+cd)

AND, OR, NOT A B C AND A1A1 A A B C OR A1A1 1 A0A0 0 A0A0 A A C NOT Review of Boolean algebra and switching functions 0 dominates in AND 1 dominates in OR

1. Identity A * 1 = A A + 1 = 1 A * 0 = 0 A + 0 = 0 2. Complement A + A’ = 1 A * A’ = 0 3. Distributive Law A(B+C) = AB + AC A+BC = (A+B)(A+C) A BCBC ACAC ABAB A BCBC ACAC ABAB

5. Associative (A+B) + C = A + (B+C) (AB)C = A(BC) C ABAB A BCBC C ABAB A BCBC 6. Demorgan’s Law(A+B)’ = A’B’ (AB)’ = A’ + B’ 7. AC + AB + BC’ = AC + BC’