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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 of which are functions of the same input variables.

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Multiple Output SOP Minimization

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  1. Multiple Output SOP Minimization

  2. 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 multiple-output minimization, but advise that all such work be performed with the aid of a computer, ie, use a CAD tool.

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

  4. Minimizing f1 f1 = B’C’ + AB’ + AC’ + A’BC

  5. Minimizing f2 f2 = A’B’C + BC’ + AB + AC’

  6. Minimizing f3 f3 = A’C + AB’ + B’C + AC’

  7. Shared Prime Implicants

  8. 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.

  9. AND-ed functions: f1.f2 f1 . f2 = AC’

  10. AND-ed functions: f2.f3 f2 . f3 = AC’ + A’B’C

  11. AND-ed functions: f3.f1 f3 . f1 = AC’ + AB’ + A’BC

  12. AND-ed functions: f1.f2 .f3 f1 . f2 . f3 = AC’

  13. Summarizing Product Terms • The original functions are: • f1 = B’C’ + AB’ + AC’ + A’BC • f2 = A’B’C + BC’ + AB + AC’ • f3 = A’C + AB’ + B’C + AC’ • The product terms, which must be included in the optimized expressions, are: • f1 . f2 . f3 = AC’ - common to all three. • f1 . f2 = AC’ • f2 . f3 = AC’ + A’B’C • f3 . f1 = AC’ + AB’ + A’BC

  14. Including Shared PI: AC’ f1 = AC’ f3 = AC’ f2 = AC’

  15. Including Shared PI: A’B’C f1 = AC’ f3 = AC’ + A’B’C f2 = AC’ + A’B’C

  16. Including Shared PI: AB’ f1 = AC’ + AB’ f3 = AC’ + A’B’C + AB’ f2 = AC’ + A’B’C

  17. Including Shared PI: A’BC f1 = AC’ + AB’ + A’BC f3 = AC’ + A’B’C + AB’ + A’BC f2 = AC’ + A’B’C

  18. Including Remaining PIs f1 = AC’ + AB’ + A’BC + B’C’ f3 = AC’ + A’B’C + AB’ + A’BC f2 = AC’ + A’B’C + AB + BC’

  19. 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.

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