DS2.CircuitModule&Verilog

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| Last Edit: 10/5/25

NAND and NOR Logic Networks

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• 这两个都是在最后的结果上加 NOT 的 Logic Network

NAND

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• 先 AND 再 NOT，写作 \(\overline {A\cdot B}\)

NOR

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• 先 OR 再 NOT，写作 \(\overline{A+B}\)

在实际制造中：NAND 和 NOR 门的晶体管布线最简单，这两个也是现实唯二的 Logic Gate

Multiplexer

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• Multiplexer, is used as a selector that S’s status can determine the output
• In case when \(s=0\), then output is whatever \(x_1\)’s value
• When \(s=1\), output is whatever \(x_2\)’s value

• Thus it has the logic of \(f=\overline sx+sy\)

Verilog Code

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A sample Verilog Structure can be the following

module Name (ports);
    specify input/output ports
    specify signal name for internal use
    assign values to outputs & signals
endmodule

Multiplexer in Verilog

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A Multiplexer can be implement as

module mux2to1 (x, y, s, f);
    input x, y, s;
    output f;
    assign f = (~s & x) | (s & y);
endmodule

• input x, y, s;: Specify the inputs
• output f;: Specify the outputs

Although x,y,s,f are variable names, in FGPA they don’t actually exist, so those are just random variable so far

• assign f = (~s & x) | (s & y);
  • ~ : NOT
  • & : AND
  • | : OR

FGPA

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FGPA, Fidd-Prog Gate Array

Multiplexer (Two to one bit)

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To implement FGPA on the FGPA, can use a Verilog Code as

module mux2to1 (SW, LEDR);
		//Specift in/outputs
    input  [9:0] SW;       
    output [9:0] LEDR;     
		//The intermediate Variables
    wire s, x, y, f;       
		//Assign
    assign s = SW[9];     
    assign x = SW[0];     
    assign y = SW[1];    
    assign f = (~s & x) | (s & y);  
    assign LEDR[0] = f;    
endmodule

Multiplexer (Two to two bits)

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A two to two bits multiplexer basically retrieve two digit input for x and y, then provide two bits output for F

module mux2to1_2bit (X, Y, S, F);
    input S;
    input [1:0] X, Y;
    output [1:0] F;

    assign F[0] = (~S & X[0]) | (S & Y[0]);
    assign F[1] = (~S & X[1]) | (S & Y[1]);
endmodule

• As seen, F has both 0 and 1 two digits

Hierarchical Verilog Code

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Verilog Code can be assigned as modules that look like functions, one module can call others for simplification

Now define a subcircuit call a 7-Segment Decoder, what is does is to get input x,x_0 and represent them as a 2 bit number

• For a 7 Segment Display, it looks like this

    h0
   ----
h5|    |h1
  | h6 |
   ----
h4|    |h2
   ----
    h3

• With 7 h, each controls one bar, and by setting them in correct, it can show number 0 - 9
• As said, before analyzing the Logic Function, always use Truth Table first

• This circuit is a 2 digit input (Four decimal numbers) input and 7 digit output function
• Its truth table can be above
• So got the logic expression for each h

h0 = ~x1 & x0
h1 = 0
h2 = x1 & ~x0
h3 = ~x1 & x0
h4 = x0
h5 = x0 | x1
h6 = ~x1

Data Structure

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In Verilog, sometimes we are cooping with decimal, sometimes binary, sometimes hex, the way to declare which one is using is by three digits

• In the case above, h1 = 0 , the way we assign 0 to h1 need the Data Structure
• For example, 0 is 1’b0
• 1 : Number of bits
• b : Base (Binary)
• 0 : Its value

Top Level Module

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Top Level Module is like a main file that connect everything

In this case, we created two two digit inputs, and use a multiplexer to choose one to display on HEX by 7 Segment Decoder, so its a circuit look like

• We have done with the multiplexer, the 7 Segment Decoder, now need to connect them

module hier (SW, HEX0);
    input  [9:0] SW;
    output [6:0] HEX0;

    wire [1:0] F;

    mux2to1_2bit U1 (SW[1:0], SW[3:2], SW[9], F);
    seg7         U2 (F, HEX0);
endmodule

• mux2to1_2bit and seg7 are the module instantiation, thus a call in main function

Half Adder

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Half Adder is a circuit that can add two 1 bit input

• When there’s two one bit adding, the highest result we get are 1 + 1 = 2
• 2 is 11 in Binary, thus this circuit is a two bit input, two bit output circuit
• Its Truth Table is

• From the truth table, we can get that
• s_1 = a & b : If both a and b are 1, then there’s a carry out（进位）
• s_0 = a^b : XOR, is one if a and b are not the same

Three input XOR

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Take three inputs and calculate their XOR

$$ f=a⊕b⊕c $$

• Basically do a^b first, then use the result to do XOR with c, it has the truth table of

• From observation, we can see that only when odd inputs are 1, the result will be 1 then
• So this is also called odd function
• In Verilog, this can be approached by assign f = a ^ b ^ c;
• For the carry out, it’s one if one of ab, ac, bc are one, so it has logic function cout = (a & b) | (a & cin) | (b & cin); , so we can conclude one Full Adder’s Verilog code be

module FA (a, b, cin, s, cout);
    input a, b, cin;
    output s, cout;

    assign s = a ^ b ^ cin;               // sum
    assign cout = (a & b) | (a & cin) | (b & cin);  // carry out
endmodule

• This FA module can due with any two 1 bit adding, it has input of a, b, cin and output s, cout
• In order to implement a three 1 bit Ripple-Carry Adder, we need to call FA three times

module adder3 (A, B, Cin, S, Cout);
    input  [2:0] A, B;
    input  Cin;
    output [2:0] S;
    output Cout;

    wire C1, C2;

    FA U1 (A[0], B[0], Cin, S[0], C1);
    FA U2 (A[1], B[1], C1, S[1], C2);
    FA U3 (A[2], B[2], C2, S[2], Cout);
endmodule

• Where c1, c2 are the middle carry out, we have the flow of

   Cin → [FA0] → C1 → [FA1] → C2 → [FA2] → Cout
             ↓          ↓          ↓
            S0         S1         S2