LOGIC GATES

 Binary information is represented in digital computers by physical quantities called signals. Electrical signals such as voltages exist throughout the computer in either one of two recognizable states. The two states represent a binary variable that can be equal to 1 or 0. For example, a particular digital computer may employ a signal of 3 volts to represent binary 1 and 0.5 volts to represent binary 0. The input terminals of digital circuits accept binary signals of 3 and 0.5 volts and the circuits respond at the output terminals with signals of 3 and 0.5 volts to represent binary input and output corresponding to 1 and 0, respectively.


GATES

Binary logic deals with binary variables and with operations that assume a logical meaning. It is used to describe, in algebraic or tabular form, the manipulation, and processing of binary information. The manipulation of binary information is done by logic circuits called gates. Gates are blocks of hardware that produce signals of binary 1 or 0 when input logic requirements are satisfied. A variety of logic gates are commonly used in digital computer systems. Each gate has a distinct graphic symbol and its operation can be described by means of an algebraic expression. The input-output relationship of the binary variables for each gate can be represented in tabular form by a truth table.

AND GATE

The names, graphic symbols, algebraic functions, and truth tables of eight logic gates are listed in Fig. 1-2. Each gate has one or two binary input variables designated by A and Band one binary output variable designated by x. The AND gate produces the AND logic function: that is, the output is 1 if input A and input B are both equal to 1; otherwise, the output is 0. These conditions are also specified in the truth table for the AND gate. The table shows that output x is 1 only when both input A and input Bare 1. The algebraic operation symbol of the AND function is the same as the multiplication symbol of ordinary arithmetic. We can either use a dot between the variables or concatenate the variables without an operation symbol between them. AND gates may have more than two inputs, and by definition, the output is 1 if and only if all inputs are I.

OR GATE

The OR gate produces the inclusive-OR function; that is, the output is 1 if input A or input B or both inputs are I; otherwise, the output is 0. The algebraic symbol of the OR function is +, similar to arithmetic addition. OR gates may have more than two inputs, and by definition, the output is 1 if any input is I.

INVERTER

The inverter circuit inverts the logic sense of a binary signal. It produces the NOT, or complement, function. The algebraic symbol used for the logic complement is either a prime or a bar over the variable symbol. The small circle in the output of the graphic symbol of an inverter designates a logic compliment. A triangle symbol by itself designates a buffer circuit. A buffer does not produce any particular logic function since the binary value of the output is the same as the binary value of the input. This circuit is used merely for power amplification. For example, a buffer that uses 3 volts for binary 1 will produce an output of 3 volts when its input is 3 volts. However, the amount of electrical power needed at the input of the buffer is much less than the power produced at the output of the buffer. The main purpose of the buffer is to drive other gates that require a large amount of power

NAND & NOR

The NAND function is the complement of the AND function, as indicated by the graphic symbol, which consists of an AND graphic symbol followed by a small circle. The designation NAND is derived from the abbreviation of NOT-AND. The NOR gate is the complement of the OR gate and uses an OR graphic symbol followed by a small circle. Both NAND and NOR gates may have more than two inputs, and the output is always the complement of the AND or OR function, respectively.

EXCLUSIVE-OR

The exclusive-OR gate has a graphic symbol similar to the OR gate except for the additional curved line on the input side. The output of this gate is I if any input is 1 but excludes the combination when both inputs are I. The exclusive-OR function has its own algebraic symbol or can be expressed in terms of AND, OR, and complement operations as shown in Fig. 1-2. The exclusive-NOR is the complement of the exclusive-OR, as indicated by the small circle in the graphic symbol. The output of this gate is 1 only if both inputs are equal to 1 or both inputs are equal to 0. A more fitting name for the exclusive-OR operation would be an odd function; that is, its output is I if an odd number of inputs are I. Thus in a three-input exclusive-OR (odd) function, the output is 1 if only one input is 1 or if all three inputs are 1. The exclusive-OR and exclusive-NOR gates are commonly available with two inputs, and only seldom are they found with three or more inputs.
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