Chapter 7Logic Circuits

Positive Logic Logic 1

high, true, on 5 Volts

Really: 2.4 to 5 Volts

Logic 0 low, false, off 0 Volts

Really: 0 to 0.4 Volts

Logic X “don’t care” Really: 0.4 to 2.4 Volts

Binary Numbers Bit a single binary digitByte 8 bitsNibble 4 bitsMegabyte 8 million bits

Transmission of Digital Information

Parallel Transmission an n-bit word is transferred on n wires

plus a common or ground wire

Serial Transmission the successive bits of a word are

transferred one after another with a single pair of wires

TTL Logic CircuitsTTL = Transistor-Transistor LogicLogic Gates AND OR NOT (inverter) NAND NOR XOR Equivalence Gate Buffer

Circuit Symbol

Truth Table

Boolean

Expression

Multiple Inputs

Numbering Systems

Binary Base 2Decimal Base 10Hexadecimal Base 16Octal Base 8

Numbering Systems Why do we use the decimal system for everyday mathematics? Answer: Fingers and Thumbs

Why do we use the binary system for computer mathematics? Answer: Computers use voltage

levels to perform mathematics. 0-Volts and 5-Volts correspond to

0’s and 1’s

CountingBinary Decimal Hexadecimal0000 0 0

To the chalk board...

Example ProblemConvert the binary number 1100 1010 to decimal and hexadecimal and octal.

More ExamplesConvert 34310 to binary and hexadecimal and octal.

Convert 1101.12 to decimal an octal.

Convert 0.39210 to binary.

Convert 317.28 to binary.

ExercisesAdd these binary numbers: 1000.111 + 1100.011

What 2 kinds of logic gates are needed for computer addition?

Boolean TheoremsAA = ?A1 = ?A0 = ?AA’ = ?A’’ = ?A(B + C) = ?

Boolean TheoremsA + A = ?A + 1 = ?A + 0 = ?A + A’ = ?

De Morgan’s Theorems(AB)’ = ?(A + B)’ = ?

(ABC)’ = ?(A + B + C)’ = ?

7.4 Synthesis of Logic GatesFind the sum-of-products for G for the truth table in Table P7.35 on page 370.Can the equation be simplified?If so, how many gates did we save?

Repeat for Table 7.7.

7.5 Minimization of Logic Gates

Find the sum-of-products for the truth table in Table 7.8 on page 352.Can the equation be simplified?How many gates did we save?

Is there a easier way to simplify these equations?

Karnaugh Mapping Steps1. Sketch a Karnaugh map grid for the

problem.2. Fill in the 1’s and 0’s from the truth

table.3. Circle groups of 1’s.4. Write an equation using these circles.

Problem P7.44, 46, 47, 48 or Table 7.49.

Chapter 7Logic CircuitsReminder: Remember to keep your graded labs for your lab portfolio.

Example ProblemWhat would be the truth table for the logic circuit shown in figure 4.18(a)?

AB Y

Example ProblemWhat would be the truth table for the logic circuit shown 14.8(b)?

AB

Y

Team Exercise – 4 MinutesWhat would be the truth table for the logic circuit shown 14.8(c)?

AB X

Y

Team Exercise – 4 MinutesWhat would be the truth table for the logic circuit shown 14.8(d)?

AB

X

Y

ExercisesP7.19P7.20P7.21,22,23

EGR215/PHY262 Seating Chart and Teams

Chris F. Trevor Michael BillyJonathan B. Carson Shaun Nathan Ignacio

Eric B. Levi Ben Charles Eric C. Chris D. Allen Chris W. Matt Wally 

    Cory Byron Tim Chris J. Matt Ryan    

    Korey Mason Shepard   JoshJonathan V.    

Note: These are the assigned teams for the SFA Rover project. Teams were assigned alphabetically and by lab section.

Kirchhoff Coulomb Boolean

Lenz Karnaugh Zener Mosfet Thevenin