International Journal of Computer Applications (0975 – 8887) Volume 62– No.6, January 2013 18 Implementation of Boolean Functions through Multiplexers with the Help of Shannon Expansion Theorem Saurabh Rawat Graphic Era University. Dehradun Anushree Sah The University of Greenwich, London, UK, Sumit Pundir Graphic Era University. Dehradun ABSTRACT Implementation of Boolean function through multiplexer can be done by various multiplexers depending upon the select lines. Implementation of Boolean functions can be done by various methods, but in this particular paper stress is more on multiplexers. Through Shannon expansion theorem,it is easy for us to implement the Boolean functions in a simpler way. Upto three variables, can be handled by multiplexers, and above that we have taken aid of look out table, and how it uses multiplexers in their operations. Keywords Multiplexers, 2 x 1, 4 x 1, 8 x 1, multiplexers, Shannon Theorem.. 1. Multiplexer A multiplexer circuit has a number of data inputs, one or more select inputs and one output . It passes the signal value on one of the data inputs to the output. Data input is selected by the values of the select inputs .Select input S, chooses as the output of the multiplexer either input x 0 or x 1 . Multiplexer’s functionality can be described in the form of a truth table. S s f 0 f 0 1 1 1.1 Graphic symbol 1.2 truth table S f 1.3 Sum of products circuit A 2 to 1 Multiplexer ( f= ) and 4 to 1 multiplexer have four data inputs x 0 ,x 1 ,x 2 , & x 3 and two select inputs S1 and S0 . The two bit number represented by S1S0 select one of the data input as output of the multiplexer. 1.4 Graphic symbol 1.5 Truth table 00 01 10 11 S 1 S 2 f 0 0 x 0 0 1 x 1 1 0 x 2 1 1 x 3 S 0 S 1 x 0 x 1 x 3 x 2 f