1. Full Adder Section 4.5 Spring, 2014 J.Ou

2. Schedule 62/3MondayBinary addition: full adder 72/5WednesdayBinary addition: full adder/four-bit adder L2/6ThursdayLab canceled 82/10MondayClass canceled 92/12Wednesday Four bit subtractor, effects of gate delay, binary multiplication L2/13ThursdayBinary adder: full adder 102/17MondayDecoder 112/19WednesdayEncoder L2/20ThursdayDecoder Experiment 122/24MondayMUX/Three state 132/26WednesdayReview L2/27ThursdayRandom number generator 143/3MondayTest 1

3. Outline Review of a Half Adder Full Adder – Explanation – Step-By-Step Module Writing Four Bit Adder

4. Derivation of ∑ BA∑ 000 101 011 110

5. Derivation of Carry Out Question: What primitive best implements C o ? Inputs: A, B Outputs: C o =A∙B BACoCo 000 100 010 111

6. Implementation of a Half-Adder

7. Limitation of a Half Adder A half-adder does not account for carry-in.

8. Truth Table for a Full Adder carry-in

9. Karnaugh Map For the Sum Bit

10. Karnaugh Map For the Carry-Out Bit

11. Implementation of a Full Adder (carry-in)

12. Build a Full-Adder Circuit w1 w2w3 M1M2

13. Module Template module module_name (,, ) endmodule Input, output wires reg Program Body

14. Module Declaration w1 w2w3 M1M2 x,y, and z are the input ports s,c are the output ports wires:x, y,z, s, c wires w1, w2, w3

15. Module Template module module_name (,, ) endmodule Input, output wires reg Program Body

16. w1 w2w3 M1M2 Use existing half adder cells Two instances: M1 and M2 Need an OR gate: I can use either primitive gates Use assign statement

17. Module Test Bench Template //`timescale 1 ms /1 us module module_tb_name (,, ) endmodule Input, output wires reg Define the test bench Call on the module

18. Modify half_adder_tb.v 1.Change `include line 2.Change module name

19. Module Test Bench Template //`timescale 1 ms /1 us module module_tb_name (,, ) endmodule Input, output wires reg Define the test bench Call on the module

20. Change input/output, wire/regs To do list: 1.Increase X,Y to X,Y,Z a.output b.t_X,t_Y, t_Z Question: Why do we have to use reg X,Y, but not wire X, Y?

21. After Modifying the Module Declaration

22. Module Test Bench Template //`timescale 1 ms /1 us module module_tb_name (,, ) endmodule Input, output wires reg Define the test bench Call on the module

23. To-Do List 1.Change output file name 2.Add Z to $fmonitor line 3.Read from three bit files 4.Update Z from t_Z 5.Change how the module is invoke.

24. Implement the To-Do List

25. Error!

26. Erroneous Output

27. Program Body w1 w2w3 M1M2

28. Output

29. Four-Bit Adder C 4 is calculated last because it takes C 0 8 gates to reach C 4. Each FA uses 2 XOR, 2 AND and 1 OR gate. A four-bit adder uses 8 XOR, 8 AND and 4 OR gate. G0G0 G1G1 G2G2 G3G3

30. Output time=230 A0=1 A1=0 A2=0 A3=1 B0=1 B1=0 B2=0 B3=1 C0=0 S0=0 S1=1 S2=0 S3=0 C4=1 time=240 A0=0 A1=1 A2=0 A3=0 B0=0 B1=0 B2=1 B3=0 C0=1 S0=1 S1=1 S2=1 S3=0 C4=0 time=250 A0=0 A1=0 A2=0 A3=1 B0=1 B1=0 B2=0 B3=0 C0=0 S0=1 S1=0 S2=0 S3=1 C4=0 time=260 A0=0 A1=1 A2=1 A3=1 B0=1 B1=1 B2=1 B3=0 C0=0 S0=1 S1=0 S2=1 S3=0 C4=1 time=270 A0=0 A1=0 A2=1 A3=0 B0=0 B1=1 B2=0 B3=0 C0=1 S0=1 S1=1 S2=1 S3=0 C4=0 time=280 A0=1 A1=0 A2=0 A3=0 B0=0 B1=0 B2=0 B3=1 C0=1 S0=0 S1=1 S2=0 S3=1 C4=0 time=290 A0=0 A1=0 A2=0 A3=0 B0=0 B1=0 B2=0 B3=0 C0=1 S0=1 S1=0 S2=0 S3=0 C4=0 time=310 A0=0 A1=0 A2=0 A3=1 B0=1 B1=0 B2=0 B3=0 C0=0 S0=1 S1=0 S2=0 S3=1 C4=0 time=320 A0=1 A1=1 A2=1 A3=0 B0=0 B1=1 B2=1 B3=1 C0=1 S0=0 S1=1 S2=1 S3=0 C4=1 time=330 A0=0 A1=1 A2=0 A3=0 B0=0 B1=0 B2=1 B3=0 C0=1 S0=1 S1=1 S2=1 S3=0 C4=0 time=340 A0=1 A1=1 A2=0 A3=1 B0=1 B1=0 B2=1 B3=1 C0=0 S0=0 S1=0 S2=0 S3=1 C4=1 time=350 A0=0 A1=1 A2=0 A3=1 B0=1 B1=0 B2=1 B3=0 C0=0 S0=1 S1=1 S2=1 S3=1 C4=0 time=360 A0=0 A1=0 A2=0 A3=0 B0=0 B1=0 B2=0 B3=0 C0=1 S0=1 S1=0 S2=0 S3=0 C4=0

31. Things to Sort Through before writing the module four_bit_adder.v – What should be declared as inputs? – What should be declared as outputs? – How do I connect the ports of four_bit_add.v module to ports of full_adder.v module? – What should be declared as wires – What verilog modules should I include? – How should the instance be invoked?

32. Things to Sort Through Before Writing the Module four_bit_adder_tb.v – What test bench should I use as a template? – What should be the output? – What wires should I have? – What should I replace t_X,t_Y, t_Z with? – How should the four_bit_adder.v be invoked? – How should the output be printed?

33. What Will Be provided? Bit files (9 files in all, downloadable from the course website) half_adder.v What you need to implement: – full_adder.v – full_adder_tb.v – four_bit_adder.v – four_bit_adder_tb.v Due date: Next Wed (2/12) in Class.