Numerical Method of Multiplexer Implementation - Examples


Example Examples

Example 1:

Consider the following function to be implemented using a multiplexer:

Figure 1

Expanding to standard sum of products form

Figure 2

Arranging in index order:

Figure 3

To obtain the data input values, all the minterms possible are listed with the data variable set as true and as false. Each minterm pair with its data variable value has a difference equal to the binary weight of the data variable. As the data variable has been chosen to be A, which has binary weight = 4, the difference is 4. The minterms corresponding to those of the required function are now bracketed.

For both terms of a pair bracketed, set the data input value to 1.
For both terms of a pair not bracketed, set the data input value to 0.
For pairs with one term bracketed, set the data input value to the data variable value.

Figure 4

Example 2:

The function is presented in decimal form and the index found. The minterms are then compared in order to find the data variable.

Figure 5

All the minterms are then listed together with the data variable set as true and false in order to find the data input values.

Figure 6

The resulting multiplexer arrangement is:

Figure 7

Alternatively one could have used a 8-line to 1-line multiplexer:

Figure 8

Example 3:

The don't care minterm in this example is listed along with the other minterms in order to find the data variable.

Figure 9

When listed with all the possible minterms the don't care condition provides two possible data input values.

Figure 10

Using 4-line to 1-line multiplexers the logic circuit is as follows:

Figure 11

There are so many inputs at either 0 or 1, is it possible to economise further? (i.e. reduce the number of integrated circuit packages). For example use an 8-line to 1-line multiplexer?

From our previous list select the two longest lists, say B and E. Therefore let B,E be the data variables.

Figure 12

The resulting logic circuit becomes:

Figure 13

1 package plus 1/2 X Quad 2-input OR gate


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Composed by David Belton - April 98