Introduction to Computer Science David Goldschmidt, Ph.D. Computer Science The College of Saint Rose CIS September 6, 2007

Binary Logic At its lowest level, a computer operates on electrical current Voltage levels indicate ON or OFF An ON state represents binary digit 1 An OFF state represents binary digit 0 We use binary logic to describe binary variables and how they are processed Such processing is done by logical circuits called gates

Logic Gates A logic gate is a logic device that accepts one or more binary inputs and produces one binary output We combine these logic gates to build integrated circuits

Integrated Circuits (i) Consider the following integrated circuit (IC): What is x when A = 0, B = 1, and C = 1 ? What is x when A = 1, B = 1, and C = 1 ? What is x when A = 0, B = 0, and C = 0 ?

Integrated Circuits (ii) Given the inputs to the following IC, what is x ?

Boolean Logic Expressions (i) We can write boolean logic expressions using the algebraic function notation from the chart

Boolean Logic Expressions (ii) Consider the following IC: The boolean logic expression is: Write the truth table _ x = AB + C

Boolean Logic Expressions (iii) Consider the following IC: The boolean logic expression is: Write the truth table _ _ x = AB(C + D)

Boolean Logic Expressions (iv) Consider the following IC: The boolean logic expression is: Write the truth table _ x = A(A + B)

Boolean Logic Expressions (v) Draw integrated circuits for the following boolean logic expressions: _ _ x = ABC _ x = AB(C + D) _ x = (A + B)(C + D) x = ABC Write truth tables for these ICs

Using the “Logg-O” Applet Access Logg-O from the Analytical Engine CD or click on the image to go to the Web: Get into teams of two or three Do Lab 7.1 and Lab 7.2 Use “print-screen” to copy your answers into a Word document