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Combinational Logic:  [Basic Gates] [Derived Gates] [The XOR Function] [Binary Addition] [Negative Numbers and Binary Subtraction] [Multiplexer] [Decoder/Demultiplexer] [Boolean Algebra] 
Sequential Logic:  [RS NAND Latch] [RS NOR Latch] [Clocked RS Latch] [RS FlipFlop] [JK FlipFlop] [D Latch] [D FlipFlop] [FlipFlop Symbols] [Converting FlipFlop Inputs] 
Alternate FlipFlop Circuits:  [D FlipFlop Using NOR Latches] [CMOS FlipFlop Construction] 
Counters:  [Basic 4Bit Counter] [Synchronous Binary Counter] [Synchronous Decimal Counter] [Frequency Dividers] [Counting in Reverse] [The Johnson Counter] 
Registers:  [Shift Register (S to P)] [Shift Register (P to S)] 
The 555 Timer:  [555 Internals and Basic Operation] [555 Application: Pulse Sequencer] 
Basic Logical Functions and Gates 

While each logical element or condition must always have a logic value of either "0" or "1", we also need to have ways to combine different logical signals or conditions to provide a logical result.
For example, consider the logical statement: "If I move the switch on the wall up, the light will turn on." At first glance, this seems to be a correct statement. However, if we look at a few other factors, we realize that there's more to it than this. In this example, a more complete statement would be: "If I move the switch on the wall up and the light bulb is good and the power is on, the light will turn on."
If we look at these two statements as logical expressions and use logical terminology, we can reduce the first statement to:
Light = Switch
This means nothing more than that the light will follow the action of the switch, so that when the switch is up/on/true/1 the light will also be on/true/1. Conversely, if the switch is down/off/false/0 the light will also be off/false/0.
Looking at the second version of the statement, we have a slightly more complex expression:
Light = Switch and Bulb and Power
Normally, we use symbols rather than words to designate the and function that we're using to combine the separate variables of Switch, Bulb, and Power in this expression. The symbol normally used is a dot, which is the same symbol used for multiplication in some mathematical expressions. Using this symbol, our threevariable expression becomes:
Light = Switch Bulb Power
When we deal with logical circuits (as in computers), we not only need to deal with logical functions; we also need some special symbols to denote these functions in a logical diagram. There are three fundamental logical operations, from which all other functions, no matter how complex, can be derived. These functions are named and, or, and not. Each of these has a specific symbol and a clearlydefined behavior, as follows:
The logic gates shown above are used in various combinations to perform tasks of any level of complexity. Some functions are so commonly used that they have been given symbols of their own, and are often packaged so as to provide that specific function directly. On the next page, we'll begin our coverage of these functions.


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