All gates using NAND gate Deriving all logic gates using NAND gates In the next post, we will design some simple combinational logic circuits using logic gates. Cross-check your designs with the designs below. It might take some time but it is necessary to practice this to get a hang of boolean logic and logic gates. Use Boolean logic and solve for the output you need. You also have equations for the gates you wish to design. You have the equation for a NAND gate and for a NOR gate. Or you can use boolean logic to obtain these. Using universal gates we can derive all the basic logic gates, EXOR gate, and their inverse gates.
How to design all gates using NAND and NOR logic gates? Moreover, they are widely used in ICs because they are easier and economical to fabricate. They can be used to design any logic gate too. NAND and NOR logic gates are known as universal gates because they can implement any boolean logic without needing any other gate. Y (A nor B) = Why are NAND and NOR gates known as universal gates? The NOR function is sometimes also known as the Pierce function. So let’s take a look at the symbol and truth table for an EXNOR gate. Doing this, the only change in the symbols for the resulting logic gates is that we put a bubble at the output to indicate that the output shall be opposite to that of the regular output of the gate. This will allow us to have more options of creating complex logic using essentially the same gates that we have seen so far, albeit with an inverter attached at their outputs. We can extend the functionality of the gates we have seen so far by just attaching an inverter to them. What is an EXNOR gate (XNOR)?Īn EXNOR logic gate is the opposite of the XOR gate. When you have multiple inputs, then you are supposed to apply two of those to an EXOR gate, get the output, apply that output and the third signal to another EXOR gate and so on. NOTE: The term “inequality detector” does not work when dealing with multiple inputs to an EXOR gate. Try designing this on your own and cross-check it if it’s the same as this. We can represent the EXOR operation as follows.Īs you can see, the second equation AB’ + A’B indicates that we can implement the EXOR logic using two AND gates, two NOT gates and one OR gate. However, its logic is so important to the core of boolean operations that we designate it a special symbol. Let’s take a look at the symbol and the truth table for a NOT gate. Moreover, the NOT gate is the third and final basic gate.
The inverter is one of the most important logical operators available in digital logic design. Since we only have two possible outputs, it will be the opposite of the input. The output of a NOT gate is not its input. Hence it is alternatively known as an inverter. The bulb is if either one or both of the switches are 1 or shorted.Ī NOT gate gives an output that is the inverse or opposite of its input. Similarly, the electrical equivalent of the OR gate is a circuit with two resistors in parallel connected to a bulb. We will take a look at that in the forthcoming posts. Moreover, we even represent the OR operation using the sum sign.
For larger numbers, we use a circuit known as a full adder. Hence, we can calculate the sum of two digital inputs using an OR gate. If you observe the table, the equivalent mathematical logic for the OR boolean logic is that of binary addition.
Let’s take a look at the symbol and truth table for OR gate first.įrom the truth table, we can say that the output of the OR logic or an OR gate is True or high or 1, even if either or both of A or B are 1.
The bulb is on only when both the switches are 1 or shorted.Īn OR gate implements the boolean logic OR. The OR gate is a basic gate.
Similarly, the electrical equivalent is a circuit with two resistors in series connected to a bulb. Can you now start to see how and why logic gates are important to make computers? Moreover, we even represent the AND operation using the concept of the dot product.
We will study that circuit in detail as we progress through this digital electronics course. For larger numbers, we can use the AND gate to design a circuit known as a multiplier. Hence, we can calculate the product of two digital inputs using an AND gate. If you observe the table, the equivalent mathematical logic for the AND boolean logic is that of multiplication. Using these three operators, we can make simple logical statements.įrom the truth table, we can say that the output of the AND logic or an AND gate is True or high or 1, only when A and B are 1. And these operators are the building blocks of Boolean logic. These words are quite similar to their English counterparts.