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Engin112-F07-L06-boolean

# Engin112-F07-L06-boolean - Engin112 Lectures 6,7 Binary...

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1 Maciej Ciesielski Department of Electrical and Computer Engineering 09/17/2007 Engin112 – Lectures 6,7 Binary Logic and Boolean Algebra Engin112 – 09/17/2007 2 Recap from last lecture Codes y Assignment of bit sequence to represent discrete elements y BCD code and addition y Weighted code Binary storage and registers y Register transfer operations Today’s lecture y Binary logic y Boolean algebra

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2 Engin112 – 09/17/2007 3 Register Transfer Operations Example: addition Designing digital logic is focus of rest of course Engin112 – 09/17/2007 4 Binary Logic Binary logic uses two possible values y ‘1’ and ‘0’ y ‘yes’ and ‘no’ y ‘true’ and ‘false’ y Can be represented by variables: A, B, C, x, y, z, … Logic functions modify input values y What is the minimum number of inputs? » 1 input -> pretty uninteresting, inverter or wire only » 2 inputs -> basic logic functions What are possible logic functions? y NOT, AND, OR y Others can be derived from those (NAND, XOR, etc.)
3 Engin112 – 09/17/2007 5 NOT Function Complement operation y Single input y Inverts value of input y Symbolized by prime x’ or overbar Truth table y Input combinations on the left y Output of function on the right Graphic symbol y NOT gate y Little circle indicates inversion 0 1 1 0 x' x x input output Engin112 – 09/17/2007 6 AND Function Operation to check if two conditions are met y Two inputs y Output = 1 if and only if both inputs are 1 y Symbolized by dot or absence of operator x y or xy Truth table y Needs to consider 2 2 = 4 input combinations Graphic symbol y AND gate 1 1 1 0 0 1 0 1 0 0 0 0 z y x inputs output

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4 Engin112 – 09/17/2007 7 OR Function Operation to check if at least one condition is met y Two inputs y Output = 1 if any one or both inputs are 1 y Symbolized by “plus” sign: x + y Truth table Graphic symbol y OR gate 1 1 1 1 0 1 1 1 0 0 0 0 z y x Engin112 – 09/17/2007 8 Comparison of Functions Timing diagrams (waveforms) y Horizontal axis is time ( t ) y Vertical axis shows signals, each with two different voltage levels t