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The XOR Function

Boolean Algebra

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Negative Numbers and Binary Subtraction

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Combinational Logic 

When logic gates are combined in any of a great number of ways, the output is always a direct derivation of the combination of input signals and the logic functions being performed. Such circuits perform combinational logic. They have no way to "remember" any prior combination of input signals. Such circuits perform all logical and arithmetic operations in a computer or calculator.
There are many logic functions available, but all of them can be performed using only three basic functions.
While only the basic functions are actually required, there are many combinations that are used so often that they have gained their own logic symbols and circuit design.
A very special derived function is the Exclusive OR, or XOR function.
Logical operations work by definite rules, just like mathematical operations. The rules for logical operations are collectively known as Boolean Algebra.
Performing arithmetic operations with logic gates? Yes, indeed. Here's how it works.
Binary subtraction might seem to require a different circuit from addition. But it doesn't, if we look at the requirements correctly.
How can we send two independent signals ove one wire and still keep them separate from each other?
Expanding the twoinput multiplexer to handle four signals.
Okay, we have combined our two signals. How do we separate them again when they reach their destination?
The logic is the same for four combined signals.


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