Thus the NAND and the NOR gates are commonly referred to as Universal Logic Gates. But as we can construct other logic switching functions using just these gates on their own, they are both called a minimal set of gates. The NAND and NOR gates are the complements of the previous AND and OR functions respectively and are individually a complete set of logic as they can be used to implement any other Boolean function or gate. However, we can realise all of the other Boolean functions and gates by using just one single type of universal logic gate, the NAND (NOT AND) or the NOR (NOT OR) gate, thereby reducing the number of different types of logic gates required, and also the cost. One of the main disdvantages of using the complete sets of AND, OR and NOT gates is that to produce any equivalent logic gate or function we require two (or more) different types of logic gate, AND and NOT, or OR and NOT, or all three as shown above. Note that neither the Exclusive-OR gate or the Exclusive-NOR gate can be classed as a universal logic gate as they can not be used on their own or together to produce any other Boolean function. ) so for a two input AND gate the Boolean equation is given as: Q = A.B, that is Q equals both A AND B. The AND function is represented in Boolean Algebra by a single “dot” (. In Boolean Algebra the AND function is the equivalent of multiplication and so its output state represents the product of its inputs. In mathematics, the number or quantity obtained by multiplying two (or more) numbers together is called the product. But first let us remind ourselves of the switching characteristics of the three basic logic gates, AND, OR and NOT.
Thus we can use these five sets of gates, together or individually as the building blocks to produce more complex logic circuits called combinational logic circuits. Therefore we can define the complete sets of operations of the main logic gates as follows: However, the NAND and NOR gates are classed as minimal sets because they have the property of being a complete set in themselves since they can be used individually or together to construct many other logic circuits. So by using these three Universal Logic Gates we can create a range of other Boolean functions and gates. However, the two functions of AND and OR on their own do not form a complete logic set. Similarly cascading an OR and NOT gate together will produce a NOR gate, and so on. Likewise, the set of OR and NOT can be used to create the AND function.Īny logic gate which can be combined into a set to realise all other logical functions is said to be a universal gate with a complete logic set being a group of gates that can be used to form any other logic function.įor example, AND and NOT constitute a complete set of logic, as does OR and NOT as cascading together an AND with a NOT gate would give us a NAND gate. In fact, it is possible to produce every other Boolean function using just the set of AND and NOT gates since the OR function can be created using just these two gates. As we have seen throught this Digital Logic tutorial section, the three most basic logic gates are the: AND, OR and NOT gates, and given this set of logic gates it is possible to implement all of the possible Boolean switching functions, thus making them a “full set” of Universal Logic Gates.īy using logical sets in this way, the various laws and theorems of Boolean Algebra can be implemented with a complete set of logic gates. Individual logic gates can be connected together to form a variety of different switching functions and combinational logic circuits.