Spring 2000 Computer Science 3410 - Tutorials A multiplexor is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line. The input line is selected via a set of selection lines. There are 2n input lines and n selection lines. Below is a logic diagram of a 4x1 Multiplexor and its block diagram.   A Boolean function can be implemented via a multiplexor in two methods, by manipulating its truth table or using Shannon's Expansion. There is a third, more systematic way of implementing function using MUXs. ANY boolean function of n variables can be implemented with a 2n-1-to-1 MUX. The procedure follows as such: First, express the function in its sum of minterms form. Assume that the ordered sequence of the variables is XYZW, where X is the leftmost variable (highest ordered bit). Connect the n-1 bits (YZW) to the selection lines of the MUX, with Y as the highest-order selection line. Now, consider X. It will be complemented in minterms 0 to (2n/2)-1 (the first half) while the second half of the minterms will have X uncomplemented. List the first half of the minterms in a row, the second half in another row underneath (label them X', X accordingly). Circle all the minterms of the function and then look at each column. If the two minterms are circled, the value for that input is 1. If the two minterms are not circled, the value for that input is 0. If the top minterm is circled only, then the value of that input is A'. If only the bottom minterm is circled, then the value of that input is A. It is not necessary to use the highest order bit as the data input, it is possible to use the lowest order bit. The ordering of the minterm will change. In this case, every even minterm is where the variable is complemented and every odd minterm is where it is not. Thus, even minterms are lined in the first row, while the odd minterms are in the second row. The rules above still hold. Try the MUX interactive exercise here.