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EXPERIMENT#2
Inverting Logic: NOT, NAND, &
NOR
OBJECTIVES:
Examine inverting logic circuits.
Demonstrate the characteristics of NOT, NAND, and NOR gates.
Develop truth tables for NOT, NAND, and NOR gates. DISCUSSION: The inverter (or NOT gate) represents logical complementation. A NOT gate can have only one
input and one output. The output of a NOT gate simply reverses (inverts) the logic value
presented at its input. The NOT gate can be combined with AND and OR gates to construct two
more basic gates: NAND and NOR gates. Both NAND and NOR gates are universal logic
gates, which means that either NAND gates or NOR gates can be used to construct any
combinational logic circuit. We will use gate symbols, truth tables, and Boolean equations to
demonstrate their characteristics. As with AND and OR gates, NAND and NOR gates can have
two or more inputs but only one output.
Gate Characteristics: 1.
The NOT Gate Symbol
Boolean Equation
Truth Table
P a g e 1 | 10
Because the NOT gate has only one input, the truth table has two rows. Moreover, the output
inverts the logic level of the input. In addition to the overhead bar shown above (read as “X = A-
bar’), notation for logical inversion includes the following: 2.
The NAND Gate
Symbol
Boolean Equation
Truth Table
The behavior of a NAND gate can be summarized as follows: The output is LOW only
when all the inputs are HIGH
. If one or more inputs are LOW (false or logic 0), the
output will be HIGH. Comparing the truth table for the NAND gate with that of the AND
gate, you will find out that each output of a NAND gate is exactly the opposite
(inverted) logic value of the corresponding output of an AND gate
. In fact, a NAND
gate is functionally equivalent to an AND gate cascaded with a NOT gate as shown
below.
3.
The NOR Gate
Symbol
Boolean Equation
Truth Table
As seen from the truth table, the output of a NOR gate is HIGH only when all the
inputs are LOW
. If one or more of the inputs are HIGH, then the output is LOW.
Similarly, a NOR gate can be constructed using an OR gate cascaded with a NOT gate. In
other words, a NOR gate is functionally equivalent to an OR gate followed by an
inverter.
P a g e 2 | 10
NAND and NOR gates can be used to perform some useful functions such as enabling
and disabling signals. Also, NAND and NOR gates can be used to perform the function
of a NOT gate.
PROCEDURE: Part I
1.)
Implement 3-input NAND gate, 3-input NOR gate and NOT gate using VHDL.
2.)
Define the input and output ports as following:
P a g e 3 | 10
3.)
Type the gate-equivalent VHDL code for the NAND, NOR & NOT gates between the “begin”
and “end Behavioral”
.
4.)
Use the xdc template from: https://www.xilinx.com/support/documentation/university/Vivado-
Teaching/HDL-Design/2015x/Basys3/Supporting%20Material/Basys3_Master.xdc
Copy and paste the whole text into your constraints file. Uncomment by deleting the # signs in front of the lines of switches and LEDs that we’re going to use. Modify the port names to match with port names defined in the design source as follows:
P a g e 4 | 10
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Figure 1
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