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Digital Logic Design-ch4 2010

# Digital Logic Design-ch4 2010 - Combina-onalLogic Chapter4...

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10/13/10 1 Combina-onal Logic Chapter 4 EECE 256 Dr. Sidney Fels Steven Oldridge Topics Combina-onal circuits Combina-onal analysis Design procedure simple combined to make complex adders, subtractors, converters decoders, mul-plexers comb. design with decoders and muxes 10/13/10 2 (c) S. Fels, since 2010 Combina-on Circuit Output depends only on present value of input 10/13/10 (c) S. Fels, since 2010 3 NOTE: No Memory or feedback paths

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10/13/10 2 Combina-on Circuit What happens if we add memory? 10/13/10 (c) S. Fels, since 2010 4 Combina-on Circuit What happens if we add memory? 10/13/10 (c) S. Fels, since 2010 5 Memory Elements Called a: Sequen&al Circuit ‐ output func-on of input and memory ‐ changes over -me Combina-on Circuit We’ll focus on combina-onal design first useful for designing how memory will change when making sequen-al circuits 10/13/10 (c) S. Fels, since 2010 6
10/13/10 3 Combina-onal Analysis Some-mes need to: confirm circuit does what it is supposed to reverse engineer circuit Steps (start at input and work to outputs): 1. label all outputs that are fn’ of inputs and derive Boolean expression 2. label all outputs that fn’ of inputs and labels done in step 1 and derive Boolean expressions 3. repeat un-l all outputs have Boolean fn’ 4. use subs-tu-on to get Boolean fn’ based only on inputs fill in truth table 10/13/10 (c) S. Fels, since 2010 7 Combina-onal Analysis 10/13/10 (c) S. Fels, since 2010 8 F2 = AB+AC+BC T2 = ABC T1 = A+B+C Combina-onal Analysis 10/13/10 (c) S. Fels, since 2010 9 T3 = T1 F2’ F1 = T2 + T3

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10/13/10 4 Combina-onal Analysis 10/13/10 (c) S. Fels, since 2010 10 F1 = ABC + T1 F2’ ; con-nue subs-tu-ng F1 = A’BC’ + A’B’C + AB’C’ + ABC Combina-onal Design 1. Determine the number of inputs and outputs 2. Assign symbols 3. Derive the truth table 4. Obtain simplified func-ons for each output 5. Draw the logic diagram 10/13/10 (c) S. Fels, since 2010 11 Adders most fundamental unit in computer add two numbers let’s start with binary… 10/13/10 (c) S. Fels, since 2010 12
10/13/10 5 ½ Adder Design Step 1 – # of inputs and outputs let’s start with ½ adder first i.e. let’s not worry about carry in just yet 10/13/10 (c) S. Fels, since 2010 13 0 0 1 1 + 0 1 0 1 sum 0 1 1 0 carry out 0 0 0 1 ½ Adder Design Step 2 – Assign symbol names 10/13/10 (c) S. Fels, since 2010 14 0 0 1 1 + 0 1 0 1 sum 0 1 1 0 carry out 0 0 0 1 A B S C ½ Adder Design Step 3 – Derive Truth Table 10/13/10 (c) S. Fels, since 2010 15 0 0 1 1 + 0 1 0 1 sum 0 1 1 0 carry out 0 0 0 1 A B S C A B S C 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1

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10/13/10 6 ½ Adder Design Step 4 – Derive simplified form use k‐maps, Boolean Algrebra, etc. 10/13/10 (c) S. Fels, since 2010 16 0 0 1 1 + 0 1 0 1 sum 0 1 1 0 carry out 0 0 0 1 A B S C A B S C 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 S = A + B C = AB ½ Adder Design Step 5 – Draw circuit diagram 10/13/10 (c) S. Fels, since 2010 17 0 0 1 1 + 0 1 0 1 sum 0 1 1 0 carry out 0 0 0 1 A B S C A B S C 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 S = A + B C = AB A B Full Adder We need to worry about possible carry‐in though Same procedure input: x, y, Cin output: S and Cout find TT 10/13/10 (c) S. Fels, since 2010 18 x y Cin S Cout 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

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Digital Logic Design-ch4 2010 - Combina-onalLogic Chapter4...

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