Boolean Algebra – The Answer to 1+1 is Not Always 1

Learning of laws of Boolean algebra is important to handle complex logical operations in computer technology as well as in real life situation. There are many Boolean operators including AND, OR, NOT and QUOTATION MARKS.

You know “0” and “1” are used both as logic symbols in the computer technology and as constants to denote permanent open or closed circuits respectively. However, after excessive usage of these logic gates, Boolean algebra was invented so that the number of these gates could be reduced without affecting the logic operation.

The list of instructions, rules or elements which can help in reducing the logic gates are collectively known as the Boolean algebra.

The Basics…

It is named after George Boole, the mathematical logic was first used in 1847. However it was only first called Boolean algebra in 1913. In this logical expressions the data sets are given truth values, either true or false, commonly expressed as either 1 or 0. This is the basis of all modern digital electronics and programming.

In simple terms, it is the mathematics that one has to use to analyze and simplify digital gates and circuits. Any complex Boolean expression can be simplified using these set of rules. The values given to the variables according to the Boolean Algebra are the truth values, commonly known as ‘True’ or ‘False’; where ‘True’ is equivalent to ‘1’ and ‘False’ is denoted as ‘0’.

Understanding Boolean Algebra Through Examples

So instead of placing numbers in the missing values, like you would in a normal mathematical operation of addition and multiplication, the word problems in it are based on the conjunctions, ‘and’, ‘or’ and ‘not’. It can be better understood by the following example,

Suppose you were to decide between taking the umbrella with you while going out. And you decide that in case of bad weather forecast or rain, you would take the umbrella. So, according to Boolean Algebra, the two propositions of weather are connected to the proposition of taking an umbrella with the conjunction of ‘Or’.

In this algebraic equation if any of the weather propositions is given the value of 1, then the end result would be 1. However, if both of these would be ‘False’ or ‘0’, then the resultant value would be ‘0’ too. This would translate into word problems in the following way.

1.    Raining + Bad Weather Forecast = Taking an Umbrella or 1+1=1

2.    No Raining + Bad Weather Forecast = Taking an Umbrella or 0+1=1

3.    Raining + No Bad Weather Forecast = Taking an Umbrella or 1+0 =1

4.    No Raining + No Bad Weather Forecast = Not Taking an Umbrella or 0+0 = 0

Multiple Variables and Precedence in Boolean Equations

There can be as many variables in the equation as one wishes, however, the values that are assigned to them could only be 1 or 0. One must also take care to state all the propositions in a very well structured way by using parenthesis to indicate how the statement and its meaning is composed. This well-defined order of stating the Boolean operations is known as “precedence.” As in other normal mathematical problems, the expressions that are written inside the brackets have to be solved first.

The theory behind Boolean algebra has been applied to something called a Boolean search. Boolean searches, often used in library databases, are also used by internet search engines and knowing how they work could drastically improve your chances of finding employment, by narrowing the search options and saving you time.

How do Boolean Searches Work?

To be conduct a Boolean search for a specific job, first you’ll have to be able to use Boolean operators. Simply put, Boolean operators are conjunctions or joining words used in a search to include or exclude keywords, and stop unwanted results from coming up. Here are some examples –

  • AND – both keywords have to be included in the search results; items with only one keyword will not be returned.
  • OR – pages with either one or both of the keywords will be included.
  • NOT – further helps you eliminate unwanted items.
  • USE BRACKETS OR PARANTHESES – use ( ) to create very precise searches. The phrases in brackets will be dealt with first, with the terms outside brackets being included in the search after.
  • QUOTATION MARKS – putting a phrase in quotation marks, like “global economics researcher jobs” will ensure that only pages with the entire phrase are selected, and not pages including only one of the search keywords.

Practice using these Boolean operator searches and you will immediately find your searches to be both more precise and efficient.

 


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