All digital equipment, whether simple or com- plex, is constructed of only a few basic circuits. These circuits, referred to as logic elements, perform some logic function on binary data.
The AND gate is a logic circuit that has two or more inputs and a single output. The AND gate produces an output of 1, only when all its inputs are 1s. If any of the inputs are 0s, the output is 0.
The operation of the AND gate is summarized by the bellow table . Such a table, called a truth table, shows the output for each possible input. The inputs are designated A and B. The output is designated Y.
The AND gate uses the rules of multiplication. The AND function is known for multiplication-like results. The output of an AND gate is represented by the equation Y 5 A·B or Y 5 AB. The AND function is typically represented by the two variables A and B as AB.
An oR gate produces a 1 output if any of its inputs are 1s. The output is a 0 if all the inputs are 0s. The output of a two-input OR gate is shown in the below truth table.
An OR gate performs the basic operation of addition. The algebraic expression for the output of an OR gate is Y= A + B. The plus sign designates the OR function.
The simplest logic circuit is the Not gate. It performs the function called inversion, or complementation, and is commonly referred to as an inverter.
The purpose of the inverter is to make the output state the opposite of the input state. The two states associated with logic circuits are 1 and 0. A 1 state can also be referred to as a high, to indicate that the voltage is higher than in the 0 state. A 0 state can also be referred to as a low, to indicate that the voltage is lower than in the 1 state. If a 1, or high, is applied to the input of an inverter, a 0, or low appears on its output. If a 0, or low, is applied to the input, a 1, or high, appears on its output.
A NAND gate is a combination of an inverter and an AND gate. It is called a NAND gate from the NOT-AND function it performs. The NAND gate is the most commonly used logic function. This is because it can be used to construct an AND gate, OR gate, inverter, or any combination of these functions.
below is the truth table for a two-input NAND gate. Notice that the output of the NAND gate is the complement of the output of an AND gate. Any 0 in the input yields a 1 output.
NAND gates are the most widely available gates on the market. The availability and flexibility of the NAND gate allows it to be used for other types of gates. below Figure shows how a two-input NAND gate can be used to generate other logic functions.
A NOR gate is a combination of an inverter and an OR gate. Its name derives from its NOT-OR function. Like the NAND gate, the NOR gate can also be used to construct an AND gate, an OR gate, and an inverter.
the bellow the truth table for a two- input NOR gate. Notice that the output is the complement of the OR-function output. A 1 occurs only when
0 is applied to both inputs. A 1 input produces a 0 output.
A less common but still important gate is called an exclusive oR gate, abbreviated as XoR. An XOR gate has only two inputs, unlike the OR gate, which may have several inputs. However, the XOR is similar to the OR gate in that it generates a 1 output if either input is a 1. The exclusive OR is different when both inputs are 1s or 0s. In that case, the output is a 0. below Figure shows the truth table for an XOR gate.
A buffer is a special logic gate that isolates conventional gates from other circuitry and provides a high driving current for heavy circuit loads or fanout. Fan-out refers to the number of input gates connected to a single logic gate output. Buffers provide noninverting input and output. A 1 in provides a 1 out and a 0 in provides a 0 out. below Figure shows the basic buffer truth table.