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Chapter 5 Boolean Algebra and Reduction Techniques 1
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5-5 DeMorgan’s Theorem Used to simplify circuits containing NAND and NOR gates A B = A + B A + B = A B 2
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DeMorgan’s Theorem Break the bar over the variables and change the sign between them –Inversion bubbles - used to show inversion. Use parentheses to maintain proper groupings Results in Sum-of-Products (SOP) form 3
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Figure 5.38 De Morgan’s theorem applied to NAND gate produces two identical truth tables. 4
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Figure 5.39 (a) De Morgan’s theorem applied to NOR gate produces two identical truth tables; 5
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More examples 6
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Bubble Pushing 1. Change the logic gate (AND to OR or OR to AND) 2.Add bubbles to the inputs and outputs where there were none and remove original bubbles 19
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5-7 The Universal Capability of NAND and NOR Gates An inverter can be formed from a NAND simply by connecting both NAND inputs as shown in Figure 5-68. 20
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More examples Figure 5-69 Forming an AND with two NANDs 21
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Figure 5-70, 5-71 (Equivalent logic circuit using only NANDs 22
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Fig 5-72 External connections to form the circuit of Fig 5-71. 23
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Figure 5-74 Forming a NOR with four NANDs Figure 5-73 Forming an OR from there NANDs. 24
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Discussion Point The technique used to form all gates from NANDs can also be used with NOR gates. Here is an inverter: Form an inverter from a NOR gate. 29 25
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5-8 AND-OR-INVERT Gates for Implementing Sum-of-Products Expressions 30
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AND-OR-INVERT Gates for Implementing Sum-of-Products Expressions 30 31
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