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Unformatted text preview: Digital System Design Combinational Logic Adapted from Assoc. Prof. Pradondet Nilagupta pom@ku.ac.th October 31, 2008 Digital System Design 2 Acknowledgement s This lecture note is modified from Engin112: Digital Design by Prof. Maciej Ciesielski, Prof. Tilman Wolf, University of Massachusetts Amherst and original slide from publisher October 31, 2008 Digital System Design 3 Two digital circuit types s Combinational digital circuits : r Consist of logic gates r Their current outputs are determined from the present combination of inputs . r Their operations can be specified logically by sets of Boolean functions . s Sequential digital circuits : r Employ storage elements in addition to logic gates . r Their outputs are a function of the inputs and the state of the storage elements . r Their outputs depend on current inputs and past input . r They have feedback connections . October 31, 2008 Digital System Design 4 Combinational circuits s 2 n possible combinations of input values s Specific functions r Adders , subtractors , comparators , decoders , encoders , and multiplexers s MSI circuits or standard cells October 31, 2008 Digital System Design 5 Example Combinational Circuit (1/2) s Circuit controls the level of fluid in a tank r inputs are: s HI  1 if fluid level is too high, 0 otherwise s LO  1 if fluid level is too low, 0 otherwise r outputs are: s Pump  1 to pump fluid into tank, 0 for pump off s Drain  1 to open tank drain, 0 for drain closed r input to output relationship is described by a truth table October 31, 2008 Digital System Design 6 Example Combinational Circuit (2/2) HI LO Pump Drain Schematic Representation HI 1 1 LO 1 1 Pump 1 x Drain 1 x Tank level is OK Low level, pump more in High level, drain some out inputs cannot occur Truth Table Representation October 31, 2008 Digital System Design 7 Analysis of A Combinational Circuit s make sure that it is combinational not sequential r No feedback path s derive its Boolean functions (truth table) s design verification s a verbal explanation of its function s Ex. What is the output function of this circuit ? October 31, 2008 Digital System Design 8 Example Analysis s Analysis steps 1. Label all gate outputs with symbols 2. Find Boolean functions for all gates 3. Express functions in terms of input variables + simplify s Substitution : F = ( T 2 T 3 ) ’ = ( ( xT 1 ) ’ ( yT 1 ) ’ ) ’ = ( xT 1 ) + ( yT 1 ) = x ( xy ) ’ + y ( xy ) ’ = = ( x ( x’ + y’ ) ) + ( y ( x’ + y’ ) ) = xx’ + xy’ + yx’ + yy’ = xy’ + yx’ = x ⊕ y T 1 = ( xy ) ’ T 3 = ( y T 1 ) ’ T 2 = ( x T 1 ) ’ F=(T 2 T 3 )’ October 31, 2008 Digital System Design 9 Example (1/3) s What are the output functions F 1 and F 2 ? October 31, 2008 Digital System Design 10 Example (2/3) 1. Start with expressions that depend only on input variables : r T 2 = ABC r T 1 = A + B + C r F 2 = AB + AC + BC 2. Express other outputs that depend on already defined internal signals r T 3 = F 2 ’T 1 r F 1 = T 3 + T 2 October 31, 2008...
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 Spring '10
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