CS 320 Unit 3 Review of Digital Logic

CS 320 Unit 3 Review of Digital Logic - CS 320 Computer...

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CS 320 Computer Architecture Spring 2008 Unit 3 Digital Logic Review Furman Haddix, Ph.D. Assistant Professor Minnesota State University, Mankato
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Unit 3 Review of Digital Logic Objectives Basic Principles of Computer Component Operation Basic Boolean Operators and Truth Tables Six Gates: NOT, AND, OR, NAND, NOR, XOR Four Boolean Operators: , +, , ( ) Truth Tables Boolean Function Definitions Implementing Boolean Functions as Combinational Circuits Boolean Algebra Tanenbaum, Chapter 3
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Basic Boolean Operators Boolean and Logical Operators Similar to HLL Logical Operators However, these are bit-wise Three Basic Operators NOT – Inversion changes bit value If true(1), then false(0) If false(0), then true(1) AND If all are true (1), then true(1), else false (0) OR If any are true(1), then true(1), else false(0)
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Basic Boolean Operators and Truth Tables NOT Input A Output F 0 1 1 0 AND A B F 0 0 0 0 1 0 1 0 0 1 1 1 OR A B F 0 0 0 0 1 1 1 0 1 1 1 1
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More Boolean Operators XOR –OR – If odd number of inputs are true(1), true(1), else false(0) EQUALS – If even number of inputs are true(1), true(1), else false(0) NAND – Not AND – Inverted Output AND NOR – Not OR – Inverted Output OR eXclusive
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More Truth Tables NAND A B F 0 0 1 0 1 1 1 0 1 1 1 0 XOR A B F 0 0 0 0 1 1 1 0 1 1 1 0 NOR A B F 0 0 1 0 1 0 1 0 0 1 1 0 EQUALS A B F 0 0 1 0 1 0 1 0 0 1 1 1 AND A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 OR A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1
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Basic Gates essential to understanding memory Basic Gates and Costs Not, Inverter – 1 Transistor (2-input) Nand, Nor – 2 Transistors NOT, NAND, and NOR Gates Power Ground Input Output
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Five Basic Gates AND Gate is constructed as a NOT-NAND Cost (with 2 inputs) is 3 Transistors OR Gate is constructed as a NOT-NOR Cost (with 2 inputs) is 3 Transistors
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Cost of Gates with Inputs 2 Cost of NAND, NOR Number of Transistors = Number of Inputs Cost of AND, OR Number of Transistors = Number of Inputs + 1 Cost of XOR A B + A B = ((A B) (A B)) = NAND(NAND(A, NOT B),NAND(B, NOT A)) NAND (NAND(A, NOT B),NAND(B, NOT A)) NAND( NAND
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