Why 9 gates are called as universal gates?
1 Answer
The term "universal gate" refers to logic gates that can be used to construct any other type of logic gate or Boolean function, either alone or in combination with other gates. In digital logic design, the 9 gates most commonly referred to as universal gates are:
1. **AND Gate**
2. **OR Gate**
3. **NOT Gate**
4. **NAND Gate**
5. **NOR Gate**
6. **XOR Gate**
7. **XNOR Gate**
8. **AND-NOT Gate**
9. **OR-NOT Gate**
However, it’s important to note that when people refer to "universal gates," they usually refer specifically to **NAND** and **NOR gates**. The reason these gates are called "universal" is because, through proper combinations of NAND or NOR gates, any Boolean function can be implemented, regardless of the number of variables or complexity.
Let’s explore why NAND and NOR gates are considered universal, and then I’ll explain the role of the other gates.
### **Why NAND and NOR are Universal Gates**
1. **NAND Gate as a Universal Gate**:
- The NAND gate (NOT AND) outputs **false** only when both of its inputs are true; otherwise, it outputs **true**.
- NAND is universal because it can be used to create the basic gates of AND, OR, and NOT.
- **NOT Gate**: A NAND gate can be configured to act as a NOT gate by tying both inputs together. This will give the inversion of the input.
- **AND Gate**: You can use a combination of two NAND gates to implement the AND function. The first NAND gate outputs a result, and the second one inverts that result, giving an AND behavior.
- **OR Gate**: By using NAND gates in a more complex arrangement, you can create an OR gate. Essentially, you use De Morgan’s laws to convert an OR operation into a NAND operation.
- Since you can build NOT, AND, and OR gates from NAND gates, you can construct any Boolean function using only NAND gates. This property makes the NAND gate universal.
2. **NOR Gate as a Universal Gate**:
- The NOR gate (NOT OR) outputs **true** only when both inputs are false. Otherwise, it outputs **false**.
- Like the NAND gate, NOR is also universal because it can be used to create NOT, AND, and OR gates.
- **NOT Gate**: A NOR gate can be configured to act as a NOT gate by tying both inputs together. This will give the inversion of the input.
- **OR Gate**: NOR can be used to form an OR gate by using De Morgan’s laws to convert the NOR operation into an OR.
- **AND Gate**: You can also construct AND gates using NOR gates in combination.
- Again, since NOR gates can generate NOT, AND, and OR functions, any Boolean function can be synthesized using only NOR gates, making NOR a universal gate.
### **Role of Other Gates**
While NAND and NOR gates are universally known for their ability to construct any Boolean function, the other gates mentioned also serve important roles:
1. **AND Gate**:
- The AND gate is not universal by itself because it cannot produce all Boolean operations on its own. However, it is a fundamental building block in digital logic.
2. **OR Gate**:
- Like the AND gate, the OR gate alone is not universal but is often used in combination with other gates to form more complex logic operations.
3. **NOT Gate**:
- The NOT gate by itself is a simple inverter, and while it's essential in most circuits, it is not universal since it can’t by itself perform more complex functions like AND or OR.
4. **XOR Gate (Exclusive OR)**:
- The XOR gate outputs **true** if the number of true inputs is odd, and false if the number of true inputs is even. XOR gates are useful in certain arithmetic circuits and error detection/correction but are not universal on their own.
5. **XNOR Gate (Exclusive NOR)**:
- The XNOR gate is the complement of XOR and provides true when the number of true inputs is even. It also has niche applications but is not universal by itself.
6. **AND-NOT Gate and OR-NOT Gate**:
- These gates are combinations of AND/OR with NOT operations. Although they are useful in certain logic designs, they are not considered universal because, by themselves, they cannot generate all Boolean functions.
### **Summary**
The term "universal gate" specifically applies to the **NAND** and **NOR** gates because, using just these gates, any Boolean function can be implemented, making them versatile and fundamental to digital circuit design. The other gates, while essential and widely used, are not considered universal in this sense because they can’t by themselves generate every possible Boolean function.
1. **AND Gate**
2. **OR Gate**
3. **NOT Gate**
4. **NAND Gate**
5. **NOR Gate**
6. **XOR Gate**
7. **XNOR Gate**
8. **AND-NOT Gate**
9. **OR-NOT Gate**
However, it’s important to note that when people refer to "universal gates," they usually refer specifically to **NAND** and **NOR gates**. The reason these gates are called "universal" is because, through proper combinations of NAND or NOR gates, any Boolean function can be implemented, regardless of the number of variables or complexity.
Let’s explore why NAND and NOR gates are considered universal, and then I’ll explain the role of the other gates.
### **Why NAND and NOR are Universal Gates**
1. **NAND Gate as a Universal Gate**:
- The NAND gate (NOT AND) outputs **false** only when both of its inputs are true; otherwise, it outputs **true**.
- NAND is universal because it can be used to create the basic gates of AND, OR, and NOT.
- **NOT Gate**: A NAND gate can be configured to act as a NOT gate by tying both inputs together. This will give the inversion of the input.
- **AND Gate**: You can use a combination of two NAND gates to implement the AND function. The first NAND gate outputs a result, and the second one inverts that result, giving an AND behavior.
- **OR Gate**: By using NAND gates in a more complex arrangement, you can create an OR gate. Essentially, you use De Morgan’s laws to convert an OR operation into a NAND operation.
- Since you can build NOT, AND, and OR gates from NAND gates, you can construct any Boolean function using only NAND gates. This property makes the NAND gate universal.
2. **NOR Gate as a Universal Gate**:
- The NOR gate (NOT OR) outputs **true** only when both inputs are false. Otherwise, it outputs **false**.
- Like the NAND gate, NOR is also universal because it can be used to create NOT, AND, and OR gates.
- **NOT Gate**: A NOR gate can be configured to act as a NOT gate by tying both inputs together. This will give the inversion of the input.
- **OR Gate**: NOR can be used to form an OR gate by using De Morgan’s laws to convert the NOR operation into an OR.
- **AND Gate**: You can also construct AND gates using NOR gates in combination.
- Again, since NOR gates can generate NOT, AND, and OR functions, any Boolean function can be synthesized using only NOR gates, making NOR a universal gate.
### **Role of Other Gates**
While NAND and NOR gates are universally known for their ability to construct any Boolean function, the other gates mentioned also serve important roles:
1. **AND Gate**:
- The AND gate is not universal by itself because it cannot produce all Boolean operations on its own. However, it is a fundamental building block in digital logic.
2. **OR Gate**:
- Like the AND gate, the OR gate alone is not universal but is often used in combination with other gates to form more complex logic operations.
3. **NOT Gate**:
- The NOT gate by itself is a simple inverter, and while it's essential in most circuits, it is not universal since it can’t by itself perform more complex functions like AND or OR.
4. **XOR Gate (Exclusive OR)**:
- The XOR gate outputs **true** if the number of true inputs is odd, and false if the number of true inputs is even. XOR gates are useful in certain arithmetic circuits and error detection/correction but are not universal on their own.
5. **XNOR Gate (Exclusive NOR)**:
- The XNOR gate is the complement of XOR and provides true when the number of true inputs is even. It also has niche applications but is not universal by itself.
6. **AND-NOT Gate and OR-NOT Gate**:
- These gates are combinations of AND/OR with NOT operations. Although they are useful in certain logic designs, they are not considered universal because, by themselves, they cannot generate all Boolean functions.
### **Summary**
The term "universal gate" specifically applies to the **NAND** and **NOR** gates because, using just these gates, any Boolean function can be implemented, making them versatile and fundamental to digital circuit design. The other gates, while essential and widely used, are not considered universal in this sense because they can’t by themselves generate every possible Boolean function.