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Chapter 7

Chapter 7. Logic 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 digit Byte 8 bits Nibble 4 bits Megabyte

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Chapter 7

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  1. Chapter 7 Logic Circuits

  2. 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

  3. Binary Numbers • Bit • a single binary digit • Byte • 8 bits • Nibble • 4 bits • Megabyte • 8 million bits

  4. 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

  5. TTL Logic Circuits • TTL = Transistor-Transistor Logic • Logic Gates • AND • OR • NOT (inverter) • NAND • NOR • XOR • Equivalence Gate • Buffer Circuit Symbol Truth Table Boolean Expression Multiple Inputs

  6. Numbering Systems • Binary Base 2 • Decimal Base 10 • Hexadecimal Base 16 • Octal Base 8

  7. 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

  8. Counting Binary Decimal Hexadecimal 0000 0 0 To the chalk board...

  9. Example Problem • Convert the binary number 1100 1010 to decimal and hexadecimal and octal.

  10. More Examples • Convert 34310 to binary and hexadecimal and octal. • Convert 1101.12 to decimal an octal. • Convert 0.39210 to binary. • Convert 317.28 to binary.

  11. Exercises • Add these binary numbers: 1000.111 + 1100.011 • What 2 kinds of logic gates are needed for computer addition?

  12. Boolean Theorems • AA = ? • A1 = ? • A0 = ? • AA’ = ? • A’’ = ? • A(B + C) = ?

  13. Boolean Theorems • A + A = ? • A + 1 = ? • A + 0 = ? • A + A’ = ?

  14. De Morgan’s Theorems • (AB)’ = ? • (A + B)’ = ? • (ABC)’ = ? • (A + B + C)’ = ?

  15. 7.4 Synthesis of Logic Gates • Find 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.

  16. 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?

  17. Karnaugh Mapping Steps • Sketch a Karnaugh map grid for the problem. • Fill in the 1’s and 0’s from the truth table. • Circle groups of 1’s. • Write an equation using these circles.

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

  19. Chapter 7 Logic Circuits Reminder: Remember to keep your graded labs for your lab portfolio.

  20. Example Problem • What would be the truth table for the logic circuit shown in figure 4.18(a)? A B Y

  21. Example Problem • What would be the truth table for the logic circuit shown 14.8(b)? A B Y

  22. Team Exercise – 4 Minutes • What would be the truth table for the logic circuit shown 14.8(c)? A B X Y

  23. Team Exercise – 4 Minutes • What would be the truth table for the logic circuit shown 14.8(d)? A B X Y

  24. Exercises • P7.19 • P7.20 • P7.21,22,23

  25. Lenz Karnaugh Zener Mosfet Thevenin Kirchhoff Coulomb Boolean Note: These are the assigned teams for the SFA Rover project. Teams were assigned alphabetically and by lab section.

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