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

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

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

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

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

Combinational Logic6 Example  Conversion from BCD to excess-5

Combinational Logic7 Example (Cont.)

Combinational Logic8 Example (Cont.)

Combinational Logic9 Example (Cont.)

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

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

Combinational Logic12 Full-Adder

Combinational Logic13 Full-Adder HOW?????

Combinational Logic14 4-bit Adder Implementation From course book

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

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

Combinational Logic17 4-Bit Adder and Subtractor From course book

Combinational Logic18 Binary Multiplier From course book

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

Combinational Logic20 From course book

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

Combinational Logic22 2x4 Decoder

Combinational Logic23 Internal Structure of 2x4 Decoder

Combinational Logic24 Another View

Combinational Logic25 From course book

Combinational Logic26 Example

Combinational Logic27 4x16 Decoder From course book

Combinational Logic28 Full Adder with Decoder

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

Combinational Logic30 2x1 Multiplexer

Combinational Logic31 4x1 Multiplexer

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

Combinational Logic33 Example

Combinational Logic34 Three-State Buffer

Combinational Logic35 2x1 MUX with Three-State Buffer

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

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

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

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

Combinational Logic40 Questions