TABLE 2-3. Basic Identities of Boolean Algebra T-6. Basic Identities of Boolean Algebra by Prentice-Hall, Inc.

Transcription

1 T-6 Basic Identities of Boolean Algebra TABLE 2-3 Basic Identities of Boolean Algebra ommutative 2. ( ) ( ) 3. ( ) ( ) Associative 4. ( ) 5. ( ) ( ) Distributive DeMorgan s 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

2 T-7 Minterms for Three Variables TABLE 2-6 Minterms for Three Variables Product Term Symbol m m m 2 m 3 m 4 m 5 m 6 m 7 m m m 2 m 3 m 4 m 5 m 6 m by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

3 T-8 Maxterms for Three Variables TABLE 2-7 Maxterms for Three Variables Sum Term Symbol M M M 2 M 3 M 4 M 5 M 6 M 7 M M M 2 M 3 M 4 M 5 M 6 M by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

4 T-9 Digital Logic Gates = = + AND gate OR gate (a) Graphic symbols NOT gate or inverter (AND) (OR) + (NOT) (b) Timing diagram 997 by Prentice-Hall, Inc. MANO & KIME Upper Saddle River, New Jersey 7458

5 T- Gates with More than Two Inputs A B (a) Three-input AND gate = AB A B D E = A + B + + D + E + (b) Six-input OR gate 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

6 T- Implementation of Boolean unction with Gates (a) = + + (b) = by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

7 T-2 Three-Level and Two-Level Implementation A A B B D D E (a) AB + (D + E ) E (b) AB + D + E 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

8 T-3 Two-Variable Map m m m 2 m 3 (a) (b) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

9 T-4 Three-Variable Map m m m 3 m 2 m 4 m 5 m 7 m 6 (a) (b) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

10 T-5 Three-Variable Map: lat and on a ylinder to Show Adjacent Squares (a) (b) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

11 T-6 our-variable Map W m m m 3 m 2 m 4 m 5 m 2 m 3 m 8 m 9 m 7 m 6 m 5 m 4 m m W (a) (b) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

12 T-7 our-variable Map: lat and on a Torus to Show Adjacencies W W (a) (b) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

13 T-8 Digital Logic Gates Graphics Symbols Name Distinctive shape Rectangular shape Algebraic equation Truth table AND & = OR = + NOT (inverter) = Buffer = NAND & = NOR = + Exclusive OR (OR) = = + = Exclusive NOR (NOR) = = + = 997 by Prentice-Hall, Inc. MANO & KIME Upper Saddle River, New Jersey 7458

14 T-9 Logical Operations with NAND Gates NOT AND = OR = by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

15 T-2 Alternative Graphics Symbols for NAND and NOT Gates + + = (a) AND - NOT (b) NOT OR (c) NOT 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

16 T-2 Logic Operations with NOR Gates Inverter OR + = + AND + = 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

17 T-22 Two Graphic Symbols for NOR Gate (a) OR NOT + + (b) NOT AND = by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

18 T-23 Demonstration of Positive and Negative Logic L L L L H L H L L H H H MOS Gate (a) Truth table with H and L (b) Gate block diagram (c) Truth table for positive logic (e) Truth table for negative logic (d) Positive-logic AND gate (f) Negative-logic OR gate 997 by Prentice-Hall, Inc. MANO & KIME Upper Saddle River, New Jersey 7458

19 T-24 ully omplementary MOS Gate Structure and Examples logic +V using p-type transistors rom G +V +V +V 2 n using n-type transistors G = +. logic rom G2 (a) General structure (b) NOR (c) NAND (d) NOT 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

20 T-25 Networks and ircuit for Example 2- p-channel circuit +V B: B A: A (a) n-channel switch network for A: A B: B : : (b) p-channel switch network for A n-channel circuit B (c) transistor circuit for 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

21 T-26 Transmission Gate (TG) = = = = (b) (a) TG TG (c) (d) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458

22 T-27 Selector and Exclusive-OR onstructed with Transmission Gates A TG A TG B TG TG (a) (b) A TG TG No path Path Path No path No path Path Path No path (c) 997 by Prentice-Hall, Inc. Mano & Kime Upper Saddle River, New Jersey 7458