Nand and nor as a universal gates
- 1. NAND and NOR As a universal gates Prepared by: Kaushal Shah Branch – 3rd Semester, Bio-medical engineering
- 2. What are a Universal Gate And why NAND and NOR are known as universal gates? A gate which can be use to create any Logic gate is called Universal Gate NAND and NOR are called Universal Gates because all the other gates can be created by using these gates
- 3. Proof for NAND gates Any Boolean function can be implemented using AND, OR and NOT gates In the same way AND, OR and NOT gates can be implemented using NAND gates only,
- 4. Implementation of NOT using NAND A NOT gate is made by joining the inputs of a NAND gate together. Input Output 0 1 1 0 Desired NOT Gate NAND Construction
- 5. Implementation of AND using NAND A NAND gate is an inverted AND gate. An AND gate is made by following a NAND gate with a NOT gate NAND Construction Input A Input B Output Q 0 0 0 0 1 0 1 0 0 1 1 1
- 6. Implementation of OR gate using NAND • If the truth table for a NAND gate is examined or by applying De Morgan's Laws, it can be seen that if any of the inputs are 0, then the output will be 1. To be an OR gate, Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 1NAND Construction
- 7. Implementation of NOR gate using NAND A NOR gate is simply an inverted OR gate. Output is high when neither input A nor input B is high: Input A Input B Output Q 0 0 1 0 1 0 1 0 0 1 1 0 NAND Construction
- 8. Implementation of XOR gate using NAND An XOR gate is constructed similarly to an OR gate, except with an additional NAND gate inserted such that if both inputs are high, the inputs to the final NAND gate will also be high, Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 0NAND Construction
- 9. Implementation of XNOR gate using NAND • An XNOR gate is simply an XOR gate with an inverted output: Input A Input B Output Q 0 0 1 0 1 0 1 0 0 1 1 1 NAND Construction
- 10. Proof for NOR gates Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. A NOR gate is logically an inverted OR gate Implementation of NOT gate using NOR NOT made by joining the inputs of a NOR gate. Input Output 0 1 1 0
- 11. Implementation of OR gate using NOR Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 1 • The OR gate is simply a NOR gate followed by another NOR gate Desired Gate
- 12. Implementation of AND gate using NOR Input A Input B Output Q 0 0 0 0 1 0 1 0 0 1 1 1 • an AND gate is made by inverting the inputs to a NOR gate. NOR Construction
- 13. Implementation of NAND gate using NOR NOR Construction
- 14. Implementation of XOR gate using NOR An XOR gate is made by connecting the output of 3 NOR gates (connected as an AND gate) and the output of a NOR gate to the respective inputs of a NOR gate. Input A Input B Output Q 0 0 0 0 1 1 1 0 1 1 1 0NOR Construction
- 15. Implementation of XNOR gate using NOR An XNOR gate can be constructed from four NOR gates implementing the expression "(A NOR N) NOR (B NOR N) where N = A NOR B". This construction has a propagation delay three times that of a single NOR gate, and uses more gates. Input A Input B Output Q 0 0 1 0 1 0 1 0 0 1 1 1NOR Construction