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Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

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Page 1: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–1 Application of commutative law of addition.

Thomas L. FloydDigital Fundamentals, 9e

Copyright ©2006 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

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Page 2: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–2 Application of commutative law of multiplication.

Thomas L. FloydDigital Fundamentals, 9e

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Page 3: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–3 Application of associative law of addition. Open file F04-03 to verify.

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Page 4: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–4 Application of associative law of multiplication. Open file F04-04 to verify.

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Page 5: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–5 Application of distributive law. Open file F04-05 to verify.

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Page 6: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–6

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Page 7: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–7

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Page 8: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–8

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Page 9: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–9

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Page 10: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–10

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Page 11: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–11

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Page 12: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–12

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Page 13: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–13

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Page 14: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–14

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Page 15: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–15 Gate equivalencies and the corresponding truth tables that illustrate DeMorgan’s theorems. Notice the equality of the two output columns in each table. This shows that the equivalent gates perform the same logic function.

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Page 16: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–16 A logic circuit showing the development of the Boolean expression for the output.

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Page 17: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–17 Gate circuits for Example 4–8. Open file F04-17 to verify equivalency.

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Page 18: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–18 Implementation of the SOP expression AB + BCD + AC.

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Page 19: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–19 This NAND/NAND implementation is equivalent to the AND/OR in Figure 4–18.

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Page 20: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–20 Implementation of the POS expression (A + B)(B + C + D)(A + C).

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Page 21: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–21 A 3-variable Karnaugh map showing product terms.

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Page 22: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–22 A 4-variable Karnaugh map.

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Page 23: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–23 Adjacent cells on a Karnaugh map are those that differ by only one variable. Arrows point between adjacent cells.

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Page 24: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–24 Example of mapping a standard SOP expression.

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Page 25: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–25

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Page 26: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–26

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Page 27: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–27

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Page 28: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–28

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Page 29: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–29

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Page 30: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–30

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Page 31: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–31

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Page 32: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–32

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Page 33: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–33

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Page 34: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–34

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Page 35: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–35 Example of mapping directly from a truth table to a Karnaugh map.

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Page 36: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–36 Example of the use of “don’t care” conditions to simplify an expression.

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Page 37: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–37 Example of mapping a standard POS expression.

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Page 38: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–38

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Page 39: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–39

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Page 40: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–40

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Page 41: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–41

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Page 42: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–42 A 5-variable Karnaugh map.

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Page 43: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–43 Illustration of groupings of 1s in adjacent cells of a 5-variable map.

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Page 44: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–44

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Page 45: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–45 A VHDL program for a 2-input AND gate.

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Page 46: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–46

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Page 47: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–47 Seven-segment display format showing arrangement of segments.

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Page 48: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–48 Display of decimal digits with a 7-segment device.

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Page 49: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–49 Arrangements of 7-segment LED displays.

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Page 50: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–50 Block diagram of 7-segment logic and display.

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Page 51: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–51 Karnaugh map minimization of the segment-a logic expression.

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Page 52: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–52 The minimum logic implementation for segment a of the 7-segment display.

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Page 53: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–53

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Page 54: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–54

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Page 55: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–55

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Page 56: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–56

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Page 57: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–57

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Page 58: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–58

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Page 59: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–59

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Page 60: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–60

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Page 61: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–61

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Page 62: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–62

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Page 63: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–63

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Page 64: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–64

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Page 65: Figure 4–1 Application of commutative law of addition. Thomas L. Floyd Digital Fundamentals, 9e Copyright ©2006 by Pearson Education, Inc. Upper Saddle

Figure 4–65

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Figure 4–66

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