### 1- The NAND Gate as a Universal Logic Element

The NAND gate is a universal gate because it can be used to produce the NOT, the AND, the OR, and the NOR functions.

An inverter can be made from a NAND gate by connecting all of the inputs together and creating, in effect, a single input, as shown in Fig for a 2-input gate.

An AND function can be generated by the use of NAND gates alone, as shown in Fig An OR function can be produced with only NAND gates, as illustrated in part (c). Finally. a NOR function is produced as shown in part (d).

### 2- The NOR Gate as a Universal Logic Element

Like the NAND gate, the NOR gate can be used to produce the NOT, AND. OR and NAND functions.

A NOT circuit, or inverter, can be made from a NOR gate by connecting all of the inputs together to effectively create a single input, as shown in Fig.(6-10)(a) with a 2-input example. Also, an OR gate can be produced from NOR gates, as illustrated in Fig.(6-10)(b).

An AND gate can be constructed by the use of NOR gates, as shown in Fig.(6-10)(c). In this case the  NOR gates G 1 and G 2 are used as inverters, and the final output is derived by the use of DeMorgan’s theorem as follows:

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