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Why input combinations producing output '1' are picked for forming a standard SOP (Sum of Products) expression and input combinations producing output '0' are picked for forming standard POS (Product of Sums) expression? Is there any specific reason behind it?

Sample Truth Table

From the sample truth table,

  1. Standard SOP expression is formed by picking the input combinations that produce an output of 1. (For an SOP expression input 1 is considered as A and input 0 is considered as A') i.e., Using the input combinations 011, 101, 110 and 111, SOP expression will formed as F = A'BC + AB'C +ABC' + ABC, where A' denotes A complement.

  2. Standard POS expression is formed by picking the input combinations that produce an output of 0. (For a POS expression input 0 is considered as A and input 1 is considered as A') i.e., Using the input combinations 000, 001, 010 and 100, POS expression will formed as F = (A+B+C)(A+B+C')(A+B'+C)(A'+B+C), where A' denotes A complement.

Why the terms producing output 1 are being selected for SOP form and those producing output 0 are being selected for POS form?

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    \$\begingroup\$ Consider spelling abbreviations next time, and (more to the point) explain what are "output 0/1 terms". \$\endgroup\$
    – Dmitry Grigoryev
    Commented Feb 6, 2019 at 10:25
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    \$\begingroup\$ Hope the question is clear now. \$\endgroup\$
    – user8379230
    Commented Feb 7, 2019 at 5:46
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    \$\begingroup\$ The immediate (but rather useless answer) is "by definition". Perhaps you want to know the reason why SOP and POS representations are used while POP and SOS are not. That reason is simple: POS and SOP can represent any function, while POP cannot represent F=A+B and SOS cannot represent F=A*B. \$\endgroup\$
    – Dmitry Grigoryev
    Commented Feb 7, 2019 at 13:29
  • \$\begingroup\$ Your answer is not to the point \$\endgroup\$
    – user8379230
    Commented Feb 11, 2019 at 9:12

1 Answer 1

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Study these two circuits. It may help you understand.

enter image description here

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    \$\begingroup\$ Could you please elaborate? \$\endgroup\$
    – user8379230
    Commented Feb 6, 2019 at 5:31
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    \$\begingroup\$ @user8379230 - The first circuit is SOP and the second one is POS. \$\endgroup\$
    – Michael Karas
    Commented Feb 6, 2019 at 10:16
  • \$\begingroup\$ Please go through the edited question and revert. \$\endgroup\$
    – user8379230
    Commented Feb 7, 2019 at 5:47
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    \$\begingroup\$ @user8379230 - Zero need to revert here. The answer to your question lies in understanding the equivalency of the above circuits. You will learn nothing out of this if you cannot figure this out from my answer. \$\endgroup\$
    – Michael Karas
    Commented Feb 7, 2019 at 9:09

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