Multiple Output SOP Minimization MultipleOutput Minimization Frequently practical

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Multiple Output SOP Minimization

Multiple Output SOP Minimization

Multiple-Output Minimization • Frequently, practical logic design problems require minimization of multiple-output functions all

Multiple-Output Minimization • Frequently, practical logic design problems require minimization of multiple-output functions all of which are functions of the same input variables. • This is such a tedious task that we relegate it to a computer program, eg, Espresso in the SIS package we see later in the course. • Here, we will show what needs to be considered in multipleoutput minimization, but advise that all such work be performed with the aid of a computer, ie, use a CAD tool.

Example of Multiple-output Minimization • To illustrate multiple-output minimization, consider the following three output

Example of Multiple-output Minimization • To illustrate multiple-output minimization, consider the following three output expressions, each of three variables:

Minimizing f 1 = B’C’ + AB’ + AC’ + A’BC

Minimizing f 1 = B’C’ + AB’ + AC’ + A’BC

Minimizing f 2 = A’B’C + BC’ + AB + AC’

Minimizing f 2 = A’B’C + BC’ + AB + AC’

Minimizing f 3 = A’C + AB’ + B’C + AC’

Minimizing f 3 = A’C + AB’ + B’C + AC’

Shared Prime Implicants

Shared Prime Implicants

Using Shared PIs • The object is to minimize each of the three functions

Using Shared PIs • The object is to minimize each of the three functions in such a way as to retain as many shared terms between them as possible, thus optimizing the combinational logic of this system. • Hence, we now need to look at the shared terms.

AND-ed functions: f 1. f 2 = AC’

AND-ed functions: f 1. f 2 = AC’

AND-ed functions: f 2. f 3 = AC’ + A’B’C

AND-ed functions: f 2. f 3 = AC’ + A’B’C

AND-ed functions: f 3. f 1 = AC’ + AB’ + A’BC

AND-ed functions: f 3. f 1 = AC’ + AB’ + A’BC

AND-ed functions: f 1. f 2. f 3 = AC’

AND-ed functions: f 1. f 2. f 3 = AC’

Summarizing Product Terms u The original functions are: u f 1 = B’C’ +

Summarizing Product Terms u The original functions are: u f 1 = B’C’ + AB’ + AC’ + A’BC u f 2 = A’B’C + BC’ + AB + AC’ u f 3 = A’C + AB’ + B’C + AC’ u The product terms, which must be included in the optimized expressions, are: u f 1. f 2. f 3 = AC’ - common to all three. u f 1. f 2 = AC’ u f 2. f 3 = AC’ + A’B’C u f 3. f 1 = AC’ + AB’ + A’BC

Including Shared PI: AC’ f 1 = AC’ f 3 = AC’ f 2

Including Shared PI: AC’ f 1 = AC’ f 3 = AC’ f 2 = AC’

Including Shared PI: A’B’C f 1 = AC’ f 3 = AC’ + A’B’C

Including Shared PI: A’B’C f 1 = AC’ f 3 = AC’ + A’B’C f 2 = AC’ + A’B’C

Including Shared PI: AB’ f 1 = AC’ + AB’ f 3 = AC’

Including Shared PI: AB’ f 1 = AC’ + AB’ f 3 = AC’ + A’B’C + AB’ f 2 = AC’ + A’B’C

Including Shared PI: A’BC f 1 = AC’ + AB’ + A’BC f 3

Including Shared PI: A’BC f 1 = AC’ + AB’ + A’BC f 3 = AC’ + A’B’C + AB’ + A’BC f 2 = AC’ + A’B’C

Including Remaining PIs f 1 = AC’ + AB’ + A’BC + B’C’ f

Including Remaining PIs f 1 = AC’ + AB’ + A’BC + B’C’ f 3 = AC’ + A’B’C + AB’ + A’BC f 2 = AC’ + A’B’C + AB + BC’

What have we learnt? • Multiple-output minimization is not for the faint hearted. •

What have we learnt? • Multiple-output minimization is not for the faint hearted. • You should be able to find reasonably good solutions from 5 -variable Kmaps. • Good understanding of these principles will help you to understand how software for SOP minimization works, coming very soon • For any practical problem, use a suitable CAD package. • The principles illustrated above are used to create efficient programs for multiple-output minimization.