This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Digital System Design Combinational Logic Adapted from Assoc. Prof. Pradondet Nilagupta [email protected] 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...
View
Full Document
 Spring '10
 SuleymanTosun
 Full adder, Binary numeral system, Binarycoded decimal

Click to edit the document details