Page 42 - Handout Digital Electronics
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Figure 4: Product of sums (POS) logic circuit for F = (A + B + C)(A + B + C)(A + B + C )
(iii) To show that the SOP and POS are the same the values of F should be the same in the truth table
which ever form is used. In the SOP truth table F=1 in the following input combinations: 001, 010, 011,
101, and 110. Any one of these input combinations can be traced on the logic circuit or substituted on
the POS form of Boolean function.
F = (A + B + C)(A + B + C)(A + B + C ) . Taking the first input combination (000)
F = (0+0+0) ∙ (1+0+0) ∙ (1+1+0)
F = (0) ∙ (1) ∙ (1) = 0
F = (A + B + C)(A + B + C)(A + B + C ) Taking input combination (101)
F = (1+0+1) ∙ (0+1+1) ∙ (0+1+0)
F = (1) ∙ (1) ∙ (1) = 1
It is clear the value of F remains the same
regardless of which Boolean form is used.
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