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Combinational Logic1 DIGITAL LOGIC DESIGN by Dr. Fenghui Yao Tennessee State University Department of Computer Science Nashville, TN

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Combinational Logic2 Remember Combinational The outputs depend only on the current input values It uses only logic gates Sequential The outputs depend on the current and past input values It uses logic gates and storage elements Network............ Inputs Outputs

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Combinational Logic3 Notes If there are n input variables, there are 2^n input combinations For each input combination, there is one output value Truth tables are used to list all possible combinations of inputs and corresponding output values

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Combinational Logic4 Basic Combinational Circuits Adders Multipliers Multiplexers Decoders Encoders Comparators Subtractors

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Combinational Logic5 Design Determine the inputs and outputs Assign a symbol for each Derive the truth table Get the simplified boolean expression for each output Draw the network diagram

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Combinational Logic6 Example Conversion from BCD to excess-5

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Combinational Logic7 Example (Cont.)

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Combinational Logic8 Example (Cont.)

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Combinational Logic9 Example (Cont.)

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Combinational Logic10 Adders Essential part of every CPU Half adder (Ignore the carry-in bit) It performs the addition of two bits Full adder It performs the addition of three bits

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Combinational Logic11 Half-Adder You can use K-Map to simplify It is also obvious from the truth table

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Combinational Logic12 Full-Adder

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Combinational Logic13 Full-Adder HOW?????

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Combinational Logic14 4-bit Adder Implementation From course book

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Combinational Logic15 Question How can you get 32-bit implementation?

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Combinational Logic16 Binary Subtractor Remember You need to take 2’s complement to represent negative numbers A-B Take 2’s complement of B and add it to A Take 2’s complement of B and add it to A First take 1’s complement and add 1

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Combinational Logic17 4-Bit Adder and Subtractor From course book

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Combinational Logic18 Binary Multiplier From course book

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Combinational Logic19 Comparators Compare two input words Returns 1 if A=B, 0 otherwise

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Combinational Logic20 From course book

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Combinational Logic21 Decoder n by 2^n decoder Converts information from n input lines into 2^n output lines 2x4 Decoder 3x8 Decoder

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Combinational Logic22 2x4 Decoder

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Combinational Logic23 Internal Structure of 2x4 Decoder

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Combinational Logic24 Another View

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Combinational Logic25 From course book

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Combinational Logic26 Example

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Combinational Logic27 4x16 Decoder From course book

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Combinational Logic28 Full Adder with Decoder

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Combinational Logic29 Multiplexers You can select information from one of many input lines and assign it to one output line You have input lines, control lines, and one output line It is called MUX

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Combinational Logic30 2x1 Multiplexer

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Combinational Logic31 4x1 Multiplexer

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Combinational Logic32 Boolean Function Implementation How do you implement it with 8x1 MUX?

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Combinational Logic33 Example

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Combinational Logic34 Three-State Buffer

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Combinational Logic35 2x1 MUX with Three-State Buffer

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Combinational Logic36 Shifters 8-input, 8-output shifter C=1 => right shift, C=0 => left shift

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Combinational Logic37 Study Problem Course Book Chapter – 4 Problems 4 – 31 Construct a 16x1 multiplexer with two 8x1 and one 2x1 multiplexer. Use block diagrams Construct a 16x1 multiplexer with two 8x1 and one 2x1 multiplexer. Use block diagrams

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Combinational Logic38 Study Problem Course Book Chapter – 4 Problems 4 – 34

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Combinational Logic39 Study Problems Course Book Chapter – 4 Problems 4 – 1 4 – 4 4 – 6 4 – 11 4 – 20 4 – 21 4 – 25 4 – 32 4 – 33 4 – 35

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Combinational Logic40 Questions

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