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Boolean search

A search for data that meets several criteria by using the Boolean operators AND, OR and NOT (see Boolean logic). For example, the request: "Search for all Spanish and French speaking employees who have MBAs" would be written as follows if the query were expressed on a command line. Spanish and French are placed in parentheses in order to be treated as a single item.


 list for degree="MBA" and
 (language="Spanish" or language="French")


In the following example, the parentheses are missing, and the query is incorrect. The AND ties MBA and Spanish together; therefore, people who speak Spanish and have an MBA would be selected, which is correct. However, the OR separates French from the rest of the query, and anyone speaking French, no matter which degree they held, would also be selected.


 list for degree="MBA" and
 language="Spanish" or language="French"





A Google "Advanced" (Boolean) Search
Searching text on Web pages is much less exact than querying records in a database, and this search actually produced 10 million results. However, the Boolean concept does still apply. In this Google "Advanced Search," the OR is stated clearly, but the AND and NOT operators are there nonetheless.






Boolean logic

The "mathematics of logic," developed by English mathematician George Boole in the mid-19th century. Its rules govern logical functions (true/false) and are the foundation of all electronic circuits in the computer. As add, subtract, multiply and divide are the primary operations of arithmetic, AND, OR and NOT are the primary operations of Boolean logic. Boolean logic is turned into logic gates on the chip, and the logic gates make up logic circuits that perform functions such as how to add two numbers together.

Various permutations of AND, OR and NOT are used, including NAND, NOR, XOR and XNOR. The rules, or truth tables, for AND, OR and NOT follow. See Boolean search, binary, logic gate and Bebop to the Boolean Boogie.





Curious About the Chip?
Wired in patterns of Boolean logic and in less space than a postage stamp, transistors in one of today's high-speed chips collectively open and close quadrillions of times every second. If you are curious about how it really works down deep in the layers of the silicon, read the rest of "Boolean logic," then "chip" and, finally, "transistor." It is a fascinating venture into a microscopic world.

The following AND, OR and NOT examples use mechanical switches to show open and closed transistors. The switching part of an actual transistor is solid state (see transistor).




An AND Gate (Wired in Series)
AND requires both inputs to be present in order to provide output. When both inputs pulse both switches closed, current flows from the source to the output.






An OR Gate (Wired in Parallel)
OR requires only one of the two inputs to be present in order for current to flow from the source to the output.






A NOT Gate (Input Is Reversed)
No pulse in puts current out (as shown). A pulse in puts no current out, as follows: an input pulse closes switch #1 and the current goes to #2. Switch #2 is normally closed, and a pulse from #1 opens it and stops the flow.






The Hierarchy
The gates make up circuits, and circuits make up logical devices, such as a CPU. We're going to look at a circuit that is present in every computer. It adds one bit to another.






Adding Two Bits Together
The half-adder circuit adds one bit to another and yields a one-bit result with one carry bit. This circuit in combination with a shift register, which moves over to the next bit, is how a string of binary numbers are added. This diagram shows the four possible binary additions for two bits.






The Half-Adder Circuit
Trace the current through the example above. See how AND, OR and NOT react to their inputs. The 1 is represented in red (flow of current), and the 0 in blue (no current). Try it yourself below.










Try It Yourself
Print this diagram and try your Boolean skill. Review the combinations of 0 and 1 above and pick any pair. With a pen or pencil, draw a line to represent a 1. Draw nothing for 0, and see if you can get the right answer.






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