What is Logic Gate in Boolean Algebra - Computer Science

What is Logic Gate and Combination Circuits

Aristotle, the founder of European logic and later mathematician Labriz, believed that the fundamental principles of logic could be expressed in mathematical language.  Then the scientist George Boole (George Boole 1815-1864) was able to successfully express this concept of logic in mathematical language.  George Boole through his various research papers established rational algebra with new ideas which later came to be known as Boolean algebra.  In 1904, Huntington (I. V. Huntington) defined Boolean algebra by making postulates of Boolean algebra.  Boolean algebra was first used in practical terms by Claude Shannon.  Shannon was the first to apply switching algebra.  Switch-on is denoted by 1 and Switch-off is denoted by 0.

Logic of Switch in Boolean Algebra

In general algebra we use functions like +, - and ÷ etc.  But of Boolean algebra. Functions like AND, OR and NOT are used in this case.  These are called logic gates.

AND Function

 An electronic circuit in which two or more switches are connected in series connection is expressed by the AND function.  The diagram or symbol of the AND gate shown in Figure 1.1 on the side has two inputs (Input) are A and B and the output is (f).  An AND gate with three inputs (A, B and C) also has a single output (f) (Figure 1.2).  AND gate can have more than three inputs.  An AND gate with N number of inputs is shown in Figure 1.3

 If the truth table of AND gate has two variables (A, B ), the number of rows in the truth table will be 22=4, the number of rows in the truth table with three variables (A, B, C) will be 2°  = 8 t.  The AND gate is the logical multiplication operation, expressed by the (.) symbol.

 In the case of AND gate, the output will be 1 only if all inputs are 1.  In all other cases the output will be 0.  Below are two truth tables for AND gates with two and three inputs.

OR Function

 An electronic circuit in which two or more switches are connected in parallel (Parallel Connection) is expressed by the OR function.

 The diagram or symbol of the OR gate shown in the adjacent figure (Figure 1.4) has two inputs (Input) are A and B and output is (f).  An OR gate with three inputs (A, B and C) also has a single output (f) (Figure 1.5).  OR gate can have more than three inputs.  A diagram of an OR gate with N number of inputs is shown in (Figure 1.6).

The OR gate is the logical addition operation, denoted by the (+) sign.  So, in case of OR gate any input will be 1 then output will be 1.  Output will be 0 only if all inputs are 0.  If the truth table of OR gate has two and three variables, the number of rows in the truth table will be 22 = 4 and 2 = 8 respectively.  Below are two truth tables for OR gates with two and three inputs.

NOT Function

 The NOT function always has one input and one output.  The output is always the exact opposite or complement of the input.  If A is the input to the NOT function, the output is Ā.  This operation is also called Complementation or Inversion.  Figure 1.7 shows the diagram of the NOT gate where A is the input and f = A is the output.

 Since the input of a NOT gate is always opposite to the output.  So, if the input is 0, the output will be 1, and if the input is 1, the output will be 0.  The truth table of the NOT gate is shown bellow.