A Guide for Online Information About:

Logic Gates

by Rick Prescott

The NOR Gate
The NOR gate is an OR gate with the output inverted. Where the OR gate allows the output to be true (logic 1) if any one or more of its inputs are true, the NOR gate inverts this and forces the output to logic 0 when any input is true.

In symbols, the NOR function is designated with a plus sign (+) and with an overbar over the entire expression to indicate the inversion. In logical diagrams, the symbol to the left designates the NOR gate. As expected, this is an OR gate with a circle to designate the inversion.

The NOR function can have any number of inputs, but practical commercial NOR gates are mostly limited to two, three, and four inputs, as with other gates in this class, to fit in standard IC packages. (More)

Truth Table: NOR

The Exclusive-OR, or XOR Gate
The Exclusive-OR, or XOR function is an interesting and useful variation on the basic OR function. Verbally, it can be stated as, "Either A or B, but not both." The XOR gate produces a logic 1 output only if its two inputs are different. If the inputs are the same, the output is a logic 0.

The XOR symbol is a variation on the standard OR symbol. It consists of a plus (+) sign with a circle around it. The logic symbol, as shown here, is a variation on the standard OR symbol.

Unlike standard OR/NOR and AND/NAND functions, the XOR function always has exactly two inputs, and commercially manufactured XOR gates are the same. Four XOR gates fit in a standard 14-pin IC package. (More)

XOR Gate
A B Q
0 0 0
0 1 1
1 0 1
1 1 0

Some common representation of logic 0 and 1 are shown in the following diagram.

Dictionary

AND Gate: In an electronic computer, a gate circuit with more than one (1) control signal (input) terminal. No output signal will be produced unless a pulse is applied to all inputs simultaneously.
Binary: There are two (2) digits (1 and 0) in the binary system instead of 10 in the decimal system. Represented in a computer circuit by the presence of current (equivalent to 1). All computer programs are executed in binary form.
Boolean Algebra: A system of mathematical logic dealing with classes, propositions, on-off circuit elements, and so forth associated by operators as AND, OR NOT, EXEPT, IF, THEN, an so on, thereby permitting computations in any mathematical system. Algebraic rules for manipulating logic equations.
Current: The movement of electrons through a conductor.
Gate: A circuit having two (2) or more inputs and one (1) output. The output depending upon the combination of logic signals as the inputs. There are four (4) gates called AND, OR, NAND, and NOR. In computer work a gate is often called an AND circuit.
Logic Circuit: A circuit (usually electronic) that provides an input-output relationship corresponding to a Boolean-algebra logic function.
Logic Diagram: A pictorial representation of interconnected logic elements using standard symbols to represent the detailed functioning of electronic logic circuits.
Logic Function: One of the Boolean-algebra functions AND, OR, and NOT or a combination of these.
NAND Gate: A combination of a NOT function and an AND function in a binary circuit that has two (2) or more inputs and one (1) output. The output is logic 0 only if all inputs are logic 1; it is logic 1 if any input is logic 0.
NOR: A function of P and Q that is true if both P and Q are false.
NOR Gate: An OR gate followed by an inverter to form a binary circuit in which the output is logic 0 if any of the inputs is logic 1 and is logic 1 only if all the inputs are logic 0.
NOT (Inverter): A circuit which takes in a positive signal and puts out a negative one or vice versa. The NOT is sometimes called an INVERTER circuit. A device or circuit that complements a Boolean function.
OR Gate: Also called OR circuit, A gate that performs the function of logic "inclusive." It produces an output whenever anyone (or more) inputs is energized.
Truth Table: A matrix which describes a logic function by listing all possible combinations of inputs, and by indicating the outputs for each combination. A listing which represents all possible input and output states of a logic function.
State: The condition of a circuit system and such. The condition at the output of a circuit that represents logic zero (0) or logic one (1).

In the LS series there are six different chips containing six different types of gates:

ý 7400 - NAND (four gates per chip)
ý 7402 - NOR (four gates per chip)
ý 7404 - NOT (four gates per chip)
ý 7408 - AND (four gates per chip)
ý 7432 - OR (four gates per chip)
ý 7486 - XOR (four gates per chip)

Inside the chips, things look like this:

Flip-flops are synchronous bistable devices. The term synchronous means the output changes state only when the clock input is triggered. That is, changes in the output occur in synchronization with the clock.
Flip-flop is a kind of multivibrator. There are three types of multivibrators:

• Monostable multivibrator (also called one-shot) has only one stable state. It produces a single pulse in response to a triggering input.
• Bistable multivibrator exhibits two stable states. It is able to retain the two SET and RESET states indefinitely. It is commonly used as a basic building block for counters, registers, and memories.
• Astable multivibrator has no stable state at all. It is used primarily as an oscillator to generate periodic pulse waveforms for timing purposes.

Edge-Triggered Flip-flops
Pulse-Triggered (Master-Slave) Flip-flops
Data Lock-Out Flip-flops
Operating Characteristics
Applications

Counters
Circuits for counting events are frequently used in computers and other digital systems. Because a counter circuit must remember its past states, it has to possess memory. The chapter about flip-flops introduced how flip-flops are connected to make a counter. The number of flip-flops used and how they are connected determine the number of states and the sequence of the states that the counter goes through in each complete cycle.

Counters can be classified into two broad categories according to the way they are clocked:

1. Asynchronous (Ripple) Counters—the first flip-flop is clocked by the external clock pulse, and then each successive flip-flop is clocked by the Q or Q' output of the previous flip-flop.
2. Synchronous Counters—all memory elements are simultaneously triggered by the same clock.

Asynchronous (Ripple) Counters
Asynchronous Decade Counters
Asynchronous Up-Down Counters
Synchronous Counters
Synchronous Decade Counters
Synchronous Up-Down Counters
Applications

More Info

Combinational Logic: [Basic Gates] [Derived Gates] [The XOR Function] [Binary Addition] [Negative Numbers and Binary Subtraction] [Multiplexer] [Decoder/Demultiplexer]

Sequential Logic: [RS NAND Latch] [Clocked RS Latch] [RS Flip-Flop] [JK Flip-Flop] [D Latch] [D Flip-Flop] [Flip-Flop Symbols] [Converting Flip-Flop Inputs]

Alternate Flip-Flop Circuits: [D Flip-Flop Using NOR Latches] [CMOS Flip-Flop Construction]

Counters: [Basic 4-Bit Counter] [Synchrounous Binary Counter] [Synchronous Decimal Counter] [Frequency Dividers] [Counting in Reverse]

Introduction to How Electronic Gates Work (How stuff Works)

Introduction to How Boolean Logic Works (How stuff Works)

Simple Gates (How stuff Works)

TTL Cookbook by Donald E. Lancaster
Introduces TTL, telling what it is and how it works. Illustrates how TTL is used in many practical applications. Provides typical circuits and working applications. Discusses TTL strategies.

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