Page 64 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 4: Minimization of Boolean Algebra

Notes
(i) (A + B )(A + ) B
(ii) AB( + CB + ) ( C)
)( +
(iii) (A + B )(A + B + CB C )
)(
(iv) (A + B + CA + B + C )(A + B + C )
Sum-Of-Products expressions are easy to generate from truth tables. All we have to do is
examine the truth table for any rows where the output is “high” (1), and write a Boolean
product term that would equal a value of 1 given those input conditions. For instance, in the
fourth row down in the truth table for our two-out-of-three logic system, where A = 0, B = 1,
and C = 1, the product term would be A′BC, since that term would have a value of 1 if and
only if A = 0, B = 1, and C = 1:

Figure 4.6: Sum-of-Products

Three other rows of the truth table have an output value of 1, so those rows also need Boolean
product expressions to represent them:

Figure 4.7: Boolean Product Expressions

Finally, we join these four Boolean product expressions together by addition, to create a single
Boolean expression describing the truth table as a whole:

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