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Digital Design Concepts: XOR Functions, Hardware Description Language

Dive into XOR functions, NAND and NOR gate implementation, multilevel circuits, parity checking, HDL, and design procedures in digital design. Includes examples and assignments for practice.

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Digital Design Concepts: XOR Functions, Hardware Description Language

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  1. CENG 241Digital Design 1Lecture 5 Amirali Baniasadi amirali@ece.uvic.ca

  2. This Lecture • Lab • Review of last lecture: Gate-Level Minimization • Continue Chapter 3:XOR functions, Hardware Description Language • HW 2: Due Thursday May 31st. • FIRST MIDTERM: THURSDAY JUNE 14, IN CLASS.

  3. Midterm 1 • CENG 241 Digital Design 1 Midterm #1 (sample) • Important Note: Show your work for all sections. • Consider the following Boolean function: • F(A, B, C, D, E) = Σ (8,10,13,15,16,18,21,23,25,27) and d(A, B, C, D, E) = Σ (0,2,5,7,29,31) • Use the 1’s in the map to find the simplest Boolean function and implement it using only NAND gates. Draw the logic.(10 points) • Use the 0’s in the map to find the simplest Boolean function and implement it using only NOR gates. Draw the logic. (10 points) • NOTE: Each gate may have up to 3 inputs.

  4. Multilevel NAND circuits • Sum of Products and Product of Sums result in two level designs • Not all designs are two-level e.g., F=A.(C.D+B)+B.C’ • How do we convert multilevel circuits to NAND circuits? • Rules • 1-Convert all ANDs to NAND gates with AND-invert symbol • 2-Convert all Ors to NAND gates with invert-OR symbols • 3-Check the bubbles, insert bubble if not compensated

  5. Multilevel NAND circuits B’ BC’

  6. Multilevel NAND circuits

  7. Exclusive-OR Function X XOR Y = X’.Y+X.Y’ two input XOR IS 1 if both inputs are not similar

  8. Three-input XOR Function F = A XOR B XOR C Multiple input XOR is 1 only if the number of 1 variables is odd: ODD function

  9. ODD Function Implementation

  10. Four-input XOR Function F detects odd number of 1s, F’ detects even number of 1’s

  11. Parity Generation and Checking • Parity bit: extra bit to ensure correct transmission of data • Parity bit is included in the message to make the number of 1s either odd (odd parity) or even (even parity). • We can use XOR to see if the number of 1’s is odd. • We can use XOR-invert to see if the number of 1’s is even. • We include the XOR output in the message • Later at receiver we check the number of 1 bits to see if the transmission is correct.

  12. Parity Generation and Checking circuits

  13. Hardware Description Language • Hardware Description Language explains hardware in textual form • Represents digital circuits • HDL has two applications: 1-Simulation: represents structure and behavior of digital circuits 2-Synthesis:Derives a list of components and interconnections from HDL. Two examples of HDL: VHDL, Verilog We use verilog since its easier to learn.

  14. Hardware Description Language-example //HDL Example 3-1 //-------------------------- //Description of the simple circuit of Fig. 3-37 module smpl_circuit(A,B,C,x,y); input A,B,C; output x,y; wire e; and g1(e,A,B); not g2(y, C); or g3(x,e,y); endmodule

  15. Hardware Description Language-example //HDL Example 3-2 //--------------------------------- //Description of circuit with delay module circuit_with_delay (A,B,C,x,y); input A,B,C; output x,y; wire e; and #(30) g1(e,A,B); or #(20) g3(x,e,y); not #(10) g2(y,C); endmodule How do we take into account gate delays?

  16. Test bench • To simulate circuits we need input signals. • The HDL description that provides the input/stimulus is called a test bench

  17. Test bench example //HDL Example 3-3 //---------------------- //Stimulus for simple circuit module stimcrct; reg A,B,C; wire x,y; circuit_with_delay cwd(A,B,C,x,y); initial begin A = 1'b0; B = 1'b0; C = 1'b0; #100 A = 1'b1; B = 1'b1; C = 1'b1; #100 $finish; end endmodule //Description of circuit with delay module circuit_with_delay (A,B,C,x,y); input A,B,C; output x,y; wire e; and #(30) g1(e,A,B); or #(20) g3(x,e,y); not #(10) g2(y,C); endmodule

  18. Test bench example simulation output

  19. Combinational Logic Combinational Logic: Output only depends on current input Sequential Logic:Output depends on current and previous inputs

  20. Design Procedure • 1.The number of inputs and outputs? • 2.Derive the truth table • 3.Obtain the Boolean Function • 4.Draw the logic diagram, verify correctness

  21. Design Procedure example • Binary Adder-Subtractor • Basic block is a half adder. • Half Adder Design: • 1.needs 2 inputs 2 outputs • 2. Truth Table: x y C S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 • 3. S=x’y+xy’ C=xy

  22. Half Adder circuit

  23. Full Adder? • Truth Table: • x y z C S • 0 0 0 0 0 • 0 0 1 0 1 • 0 1 0 0 1 • 0 1 1 1 0 • 1 0 0 0 1 • 1 0 1 1 0 • 1 1 0 1 0 • 1 1 1 1 1

  24. Full Adder Map

  25. Full Adder Circuit

  26. Full Adder Circuit Half adder ?

  27. 4-bit Adder Circuit But this is slow...

  28. Summary • Implementation, XOR, Parity Checking, HDL • Reading up to page 121-end of chapter 3 • Homework 2: problems 3-11, 3-15, 3-20, 3-23 and 3-24 from textbook

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