Background

Background - o Exclusive OR o Detects difference o Modulo 2...

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EE 2730 Fall 2009 Background EE 2720 Chapters 1-6 EE 2730 - Fall 2009

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Basic Gates o AND o OR o NOT EE 2730 - Fall 2009
Boolean Algebra x + 0 = x x.1 = x identity x.0 = 0 x + 1 = 1 zero x.x = x x + x = x idempotence x.x’ = 0 x + x’ = 1 complementation x.y = y.x x + y = y + x commutativity x.(y.z) = (x.y).z x +(y + z) = (x + y) + z associativity x.(y+z) = x.y + x.z x + y.z = (x +y).(x + z)distributivity x + xy = x(x+y) = x absorption (x’)’ = x involution (x + y)’ = x’y’ (xy)’ = x’+ y’ DeMorgan’s Laws EE 2730 - Fall 2009

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Duality in Boolean Algebra o Duality n 0 ↔ 1 n And ↔ Or o Example: x+1 = 1 n So x.0 = 0 o Example x.(y+z) = x.y + x.z n So x + y.z = (x+y)(x+z) EE 2730 - Fall 2009
NAND and NOR Gates o NAND o NOR EE 2730 - Fall 2009

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Exclusive OR/NOR

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Unformatted text preview: o Exclusive OR o Detects difference o Modulo 2 Sum EE 2730 - Fall 2009 o Driver o Tristate buffer Draw the function table Buffers EE 2730 - Fall 2009 Transmission Gate o Only one independent control o Input/output symmetric EE 2730 - Fall 2009 Binary Representations & Operations o Unsigned integers o Octal o Hexadecimal o Two’s complement o Addition o Subtraction o Multiplication o Division EE 2730 - Fall 2009 Karnaugh Map EE 2730 - Fall 2009 Don’t Cares EE 2730 - Fall 2009 Multiplexer o 2-to-1 o 4-to-1 EE 2730 - Fall 2009 Decoder o 2-to-4 (1-hot decoder) EE 2730 - Fall 2009 Adders o Look up Sections 5.2 EE 2730 - Fall 2009...
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