Modeling of Universal and Special Gates on Verilog

Modeling of Universal and Special Gates on Verilog

In this write-up, we discuss the remaining Gates, which structure the foundation of Digital Electronics, i.e., Modeling of Universal and Special Gates on Verilog. We have already covered each topic related to it. So visit them all in Verilog Catagory.

See the first part: Modeling Basic Gates through Verilog

Universal Gates

 The NAND gate and NOR gate are called Universal gates because they can perform all the three essential functions of AND, OR, and NOT gates. Furthermore, these two gates realize all other gates.

NAND Gate

The NAND gate is an AND gate followed by NOT gate. Thus, we can say it is a NOT-AND operation. It may have two or more inputs but only one output. Below is the logical symbol of a NAND gate and the truth table.

Logical symbol of NAND Gate
Logical symbol of NAND Gate
Input AInput BOutput C
001
011
101
110

The logic expression of output is C= (A.B)’ = A’ +B’ (by de morgan’s theorem)

It is clear from the truth table of the two-input NAND gate that the output is High when either A or B or when both the inputs are Low. We can say that, if both A’ and B’ are High, then the output is High. Therefore, the NAND gate can perform the OR function by inverting the inputs and then ORing it. In conclusion, the NAND Gate and AND Gate are complementary for a given number of inputs.  The OR gate with inverted inputs is called bubbled OR gate or negative OR gate. The NAND gate is also called an active low OR gate.

Design Module

//Gate Level Modeling
module nandgate(output reg c, input a,b);
nand  a1(c,a,b);
endmodule
//Data Flow Modeling
module nandgate (output reg c, input a,b);  // data type can be declared in port list
assign c = ~(a & b);  // (~) is the symbol for inverter
endmodule
//Behavioral Modeling
module nandgate(c,a,b);
output reg c;
input a,b;
[email protected] (*) // can be replaced by [email protected](a or b)
begin
if(a==1 && b==1)
begin
c=0;
end
else
c=1;
end
endmodule

Test Bench

module nandgate_tb;
wire t_c;
reg t_a,t_b;
nandgate dut(t_c, t_a, t_b);
initial               // can be used with single function
$monitor(t_a,t_b,t_c); 
initial
$display("a=%b, b=%b ,c=%b",t_a,t_b,t_c); // same as printf in C programming 
                                             language
initial  //can be used with clubbed functions
begin
$dumpfile("dump.vcd");
$dumpvars;
end
initial
begin
t_a=0;
t_b=0;
#50
t_a=0;
t_b=1;
#50
t_a=1;
t_b=0;
#50
t_a=1;
t_b=1;
end
endmodule
Modeling of Universal and Special Gates on Verilog: The waveform of NAND Gate
The waveform of NAND Gate

NOR Gate

OR gate and NOT gate merges to make NOR Gate. So we can say it is a NOT-OR operation. It may certainly have two or more inputs and an output. Listed below are the symbol and the truth table of the gate.

Logical Symbol of NOR Gate
Logical Symbol of NOR Gate
Input AInput BOutput C
001
010
100
110

Truth table clears that the output is one’ only if all the inputs are at logic zero. We can also say that if the inputs A’ =B’ =High, then the output C is High. Thus, the NOR gate is equivalent to AND gate with inverted inputs, and it can be realized by a bubbled AND gate. Active LOW AND gate is the other name for the NOR gate.

 The logical expression for the output is

 C = (A+B)’ = A’.B’

 Design Module

//Gate level modelling
module norgate(output reg c, input a,b);
nor  a1(c,a,b);
endmodule
//Data flow modeling
module norgate (output reg c, input a,b);
assign c = ~(a + b);
endmodule
//Behavioral Modeling
module norgate(c,a,b);
output reg c;
input a,b;
[email protected] (*)
begin
if(a==0 && b==0)
begin
c=1;
end
else
c=0;
end
endmodule

Test Bench

module norgate_tb;
wire t_c;
reg t_a,t_b;
norgate dut(t_c, t_a, t_b);
initial
begin
$monitor(t_a,t_b,t_c);
$display("a=%b, b=%b ,c=%b",t_a,t_b,t_c);
$dumpfile("dump.vcd");
$dumpvars;
end
initial
begin
t_a=0;
t_b=0;
#50
t_a=0;
t_b=1;
#50
t_a=1;
t_b=0;
#50
t_a=1;
t_b=1;
end
endmodule
The waveform of NOR Gate
The waveform of NOR Gate

The Exclusive OR gate and Exclusive NOR gate is known as Special function gates. Though they can be realized using Universal gates, their unique application in electronics make them special.

EX-OR Gate

A basic EX-OR gale is a two-input single-output logic gate whose output is assumed to be HIGH only when it’s one of the inputs is High. The logic symbol and the truth table for a two-input EX-OR gate are shown respectively.

Logical Symbol of XOR Gate
Logical Symbol of XOR Gate
Input AInput BOutput C
000
011
101
110

 If the input variables are represented by A and B, then the logical expression for output is C=A’B+AB’ = A ⊕ B

Practically, three or more input EX-OR gate does not exist. But when more than two variables are EXORed, a number of two input EX-OR gate is used. There, the output is assumed to be one when an odd number of input variables is one. That is why the Ex-OR gate is known as the odd number of one’s detector in the input. The most crucial application of the EX-OR gate is in ‘parity generation and detection. It is also known as the “staircase switch.”

Design Module

//Gate Level Modeling
module exor(output reg c, input a,b);
xor a1(c,a,b);
endmodule
//Data Flow Modeling
module exor(output reg c, input a,b);
assign c = a^b;
endmodule
//Behavioral Modeling
module exor(c,a,b);
output reg c;
input a,b;
[email protected] (*)
begin
if(a==b)
begin
c=0;
end
else
c=1;
end
endmodule

Test Bench

module exor_tb;
wire t_c;
reg t_a,t_b;
exor dut(t_c, t_a, t_b);
initial
$monitor(t_a,t_b,t_c);
initial
$display("a=%b, b=%b ,c=%b",t_a,t_b,t_c);
initial
begin
$dumpfile("dump.vcd");
$dumpvars;
end
initial
begin
t_a=0;
t_b=0;
#50
t_a=0;
t_b=1;
#50
t_a=1;
t_b=0;
#50
t_a=1;
t_b=1;
end
endmodule
The waveform of EX-OR Gate
The waveform of EX-OR Gate

EX-NOR Gate

Modeling of Universal and Special Gates EX-NOR on Verilog. An EX-NOR gate is an EX-OR gate followed by NOT gate. The EX-NOR gate is two inputs and one output logic circuit in which the output is 1 only when both the inputs are the same. Thus, it is also called as “gate of equivalence” or “coincidence logic”. Diagram and truth table of two-input EX-NOR gate are shown.

Logical Symbol of XNOR Gate
Logical Symbol of XNOR Gate
Input AInput BOutput C
001
010
100
111

Thus, for input variables A and B the logical expression for the output of an EX-NOR gate is given, C = AB+ A’B’ =A ʘ B

Practically, three or more variable EX-NOR gate does not exist. However, if the number of variables has to be EX-NORED, then a number of two variable EX-NOR gates will be used in which the output is high for even number of input variables is one. Thus, it is also known as “even number of one’s detector”. When the number of input variables is odd, then it is also known as an “odd number of one’s detector”.

Design Module

//Gate Level Modeling Special Gates through Verilog
module exnor(output reg c, input a,b);
xnor a1(c,a,b);
endmodule
//Data Flow Modeling
module exnor(output reg c, input a,b);
assign c = ~(a ^ b);
endmodule
//Behavioral Modeling
module exnor(c,a,b);
output reg c;
input a,b;
[email protected] (*)
begin
if(a==b)
begin
c=1;
end
else
c=0;
end

Test Bench

module exnor_tb;
wire t_c;
reg t_a,t_b;
exnor dut(t_c, t_a, t_b);
initial
$monitor(t_a,t_b,t_c);
initial
$display("a=%b, b=%b ,c=%b",t_a,t_b,t_c);
initial
begin
$dumpfile("dump.vcd");
$dumpvars;
end
initial
begin
t_a=0;
t_b=0;
#50
t_a=0;
t_b=1;
#50
t_a=1;
t_b=0;
#50
t_a=1;
t_b=1;
end
endmodule
Modeling of Universal and Special Gates on Verilog: The waveform of EX-NOR Gate
The waveform of EX-NOR Gate

BUFFER

In novice language, a buffer means a temporary barrier. Its application certainly remains the same in digital electronics. A buffer is used to transfer a signal from input to output unchanged. In other words, it is the opposite of the inverter. However, the output will be the same as the input and use to increase the propagation delay.

Logical Symbol of Buffer
Logical Symbol of Buffer
Input aOutput b
00
11

Design Module

module bufdes(y,a);
input a;
output reg b;
assign b = a;	
endmodule

Test Bench

module buf_tb;
reg a;
wire b;
bufdes dut(b,a);
initial
begin
$display (a,b);
$monitor(a,b);
$dumpfile("dump.vcd");
$dumpvars;
end
endmodule
The waveform of Buffer

Transmission Gate

Firstly, we shall see the basics of CMOS. A complementary MOSFET is a combination of p-type MOSFET and n-type MOSFET. Term complimentary here means using complementary MOSFETs to perform a logical operation. CMOS devices are popular because they have high speed, low power consumption, and noise immunity.

Transmission door (TG) or pass gate is a basic switch circuit comprising of one NMOS and one PMOS transistor, associated in equal. Complementary gate voltages are applied to both the transistors.

The TG works as a bidirectional switch between the hubs A and B. Additionally, signal C constrains them. In the event that the control signal C is logic high, i.e., equivalent to voltage – at that point, the two transistors are turned on and give a low resistance current way between the hubs A and B. In the event that the control signal C is low, at that point the two transistors will be off, and the way between the hubs A and B will be an open circuit.

Symbol of Transmission Gate
Symbol of Transmission Gate
ControlInput aOutput y
pMOSnMOS
0100
11
100z
1z

‘z’ signifies high impedance or infinitely high resistance.

Design Module

module transgate(y,c,a);
output reg y;
input a,c ;
input wire cbar;
assign cbar = ~c;
cmos cm(y,a,c,cbar);
endmodule

Cmos is already declared in the Verilog. NMOS and PMOS combine to make CMOS. So, the code line CMOS

CMOS cm (y, a, c, cbar);   has the below alternate way of modeling as:

nmos(y, a, c);

pmos (y, a, cbar);

Test Bench

module transmissiongatetb;
wire y;
reg a,c;
transgate dut(y,c,a);
initial
begin
$display ("\ta\ty",a,y);
a = 0; c = 0; # 50
a = 1; c = 0; # 50
a =0; c = 1; # 50
a = 1; c = 1;
end
//enabling the wave dump
initial 
begin
$dumpfile("dump.vcd"); 
$dumpvars;
end
endmodule
The waveform of Transmission Gate

Conclusion

In this very article: Modeling of Universal and Special Gates on Verilog, we learned about the Universal and Special Purpose gates and justified why they are named so. Additionally, we saw two other gates which have more application in advanced electronics and VLSI. From the next article, we will design the Combinational Circuit.

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