9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU1 Combinational Logic Circuits – Gates

9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU2 Class 4 outline  Binary Logic and Gates Basic Gates Implemented Gates  Material from section 2-1 of text

Basic Gates  Gates are the base level elements of digital systems.  Gates are used to implement Boolean Logic functions.  Will start with one level circuits or just a single gate.  Then move on to two or more levels of logic circuits. 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU3

Logic gates implementation  Logic gates, having two distinct and stable states, high and low, are implemented today using interconnected MOS transistors (most common).  Today CMOS – Complementary Metal Oxide Semiconductor – technology is most common.  Have had a steady progression of technology used for the implementation of digital circuits. 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU4

Past technologies  RTL – Resistor Transistor Logic – implemented with resistors and bipolar transistors  TTL – Transistor Transistor Logic – implemented with bipolar transistors  NMOS – n-type MOS transistors – implemented with one transistor configured as a MOS resistor – similar in philosophy to RTL 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU5

Basic Functions  AND Represented by a dot (·) or the absence of an operator. May be written  Z = X AND Y  z = x AND y  Z = X · Y  Z = XY Meaning: Result is TRUE if, and only if, both X and Y are TRUE Verbal– John and Mary went to the dance and to be true, they both went to the dance. 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU6

Basic Functions  OR Represented by the + operator symbol Examples  Z = X OR Y  Z = x OR Y  Z = X + Y Meaning: Result is TRUE if at least one of X and Y, or both, are TRUE. Verbal – John or Mary went to the dance. Meaning either John went to the dance, Many went to the dance, or both of them went to it. 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU7

Basic Functions  NOT Represented by a bar ¯ over the symbol or the word NOT Examples  Z = NOT X Meaning: True if X is False False if X is True 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU8

Truth table and gate symbols  AND function OR function 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU9

Truth table and gate symbols  NOT 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU10

But gates are electronic elements 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU11  And have voltages over time that are interpreted as logic values over time

Basic gates with more than 2 inputs  It is often the case that we have 3 input AND gates or 3 inputs OR gates.  Sometimes, even have 4 input gates.  Some logic equations have many terms ANDed together. In MOS these many input gates are not readily feasible. Therefore, use multiple levels of logic. 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU12

Class 4 assignment  Covered section 2.1  Problems for hand in None today  Problems for practice 2-1 do it – This is an important one  Section 2.2 9/15/09 - L4 Combinational Logic - Gates Copyright Joanne DeGroat, ECE, OSU13