1 CSCE 211H Fall 2015 Lecture 5 Combinational Components Topics Products-of-Sums Form examples 5 variable and larger Karnaugh Maps Components: Decoders, MultiplexersReadings September 21, 2015 CSCE 211 Digital Design 2 CSCE 211H Fall 2015 Overview Last Time: Boolean Algebra Continued Combinational Circuit Analysis Sums-of-Products Form Karnaugh Maps 3,4 variable maps Dont Care Conditions Products-of-Sums FormNew: Review Products-of-Sums Form (5, 6, variable maps) Decoders Multiplexers Circuits kits on paper 3 CSCE 211H Fall 2015 Karnaugh Map Simplification F(W,X,Y,Z) = YZ WX Z W X Y 4 CSCE 211H Fall 2015 Karnaugh Map Simplification F(W,X,Y,Z) = YZ WX Z W X Y 5 CSCE 211H Fall 2015 Products-of-Sums Simplification F(W,X,Y,Z) = YZ WX Z W X Y 6 CSCE 211H Fall Variable Map Simplification F(V, W,X,Y,Z) = YZ WX Z W X Y YZ WX Z W X Y 7 CSCE 211H Fall Variable Map Simplification F(V, W,X,Y,Z) = YZ WX Z W X Y YZ WX Z W X Y 8 CSCE 211H Fall Variable Map F(U,V,W,X,Y,Z) = 9 CSCE 211H Fall Variable Map F(U,V,W,X,Y,Z) = 10 CSCE 211H Fall 2015 Combinational Circuits A combinational circuit is one that The outputs are functions strictly of the inputs There are no feedback loops 11 CSCE 211H Fall 2015 12 CSCE 211H Fall 2015 13 CSCE 211H Fall 2015 14 CSCE 211H Fall 2015 15 CSCE 211H Fall 2015 16 CSCE 211H Fall 2015 17 CSCE 211H Fall 2015 18 CSCE 211H Fall x8 Decoder 19 CSCE 211H Fall 2015 20 CSCE 211H Fall x16 decoder from 2x4s 21 CSCE 211H Fall 2015 22 CSCE 211H Fall 2015 Multiplexers A multiplexer selects one of its inputs to route to its outputs. 23 CSCE 211H Fall 2015 BreadBoard 24 CSCE 211H Fall 2015 Wiring an LED + - To wire an led 1.Hook the positive to Vcc 2.Hook the negative to a 330 ohm resistor 3.Hook the resistor to Gnd 4.Check for loose wires 5.Check for shorts See section page for more details I LED = 10 mA needed to light the LED Voltage drop is about 1.6V 303 Ohms 25 CSCE 211H Fall LS00 Quad 2 input NAND 26 CSCE 211H Fall LS04 Hex Inverter 27 CSCE 211H Fall 2015 Half adder How many inputs? How many outputs? 28 CSCE 211H Fall Variable Map F(U,V,W,X,Y,Z) = 29 CSCE 211H Fall 2015 30 CSCE 211H Fall 2015 31 CSCE 211H Fall 2015 Analyze This! F1 = ? F2 = ? What are the delays? 32 CSCE 211H Fall 2015 Quick Whats This? 33 CSCE 211H Fall 2015 Whats This? 34 CSCE 211H Fall to 1 Mux from 4x1 Muxes 35 CSCE 211H Fall 2015 Big Multiplexers from smaller ones Show the design of a 32-to-1 Mux from 8-to-1s and smaller muxes 36 CSCE 211H Fall 2015 BreadBoard 37 CSCE 211H Fall 2015 Wiring an LED + - To wire an led 1.Hook the positive to Vcc 2.Hook the negative to a 330 ohm resistor 3.Hook the resistor to Gnd 4.Check for loose wires 5.Check for shorts See section page for more details I LED = 10 mA needed to light the LED Voltage drop is about 1.6V 303 Ohms 38 CSCE 211H Fall LS00 Quad 2 input NAND 39 CSCE 211H Fall LS04 Hex Inverter 40 CSCE 211H Fall 2015 Two Bit adder How many inputs? How many outputs? Do we have enough chips? 41 CSCE 211H Fall 2015 Implementing a Binary Adder Using a Decoder PCXYSC x8 Decoder PC X Y 42 CSCE 211H Fall LS139 Decoder Dual 2x4 decoder 43 CSCE 211H Fall 2015 Using a 74LS139 to implement a Half-adder XYXY SCSC 44 CSCE 211H Fall LS157 Dual 4 input Mux 45 CSCE 211H Fall 2015 Hardware Description Languages Hardware description language or HDL is any language from a class of computer languages for formal description of electronic circuits Boolean Algebra was applied to circuits by Shannon Current HDLs include: Verilog HDL Verilog HDL VHDL VHSIC HDL VHDL VHSIC HDL VHSIC Very High Speed Integrated Circuits ABEL HDL - Advanced Boolean Expression Language ABEL HDL - Advanced Boolean Expression Languageageage 46 CSCE 211H Fall 2015 Seven Segment Display Common anode Common anode 47 CSCE 211H Fall 2015 Functions for 74LS47 with dont cares a(D,C,B,A) = D + A. C + A. B + A. C b(D,C,B,A) = D + (D'*C') + (A'*B') + (A*B) c