number_system

# Each maxterm is obtained from an or term of the n

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Unformatted text preview: decimal equivalent of the binary number of the minterm designated. In a similar fashion, n variables forming an OR term, with each variable being primed or unprimed, provide 2n possible combinations called maxterms or standard sums. The eight maxterms for three variables, together with their symbolic designation, are listed in Figure 6.16. Any 2n maxterms for n variables may be determined similarly. Each maxterm is obtained from an OR term of the n variables, with each variable being unprimed if the corresponding bit is a 0 and primed if it is a 1. Note that each maxterm is the complement of its corresponding minterm and vice-versa. Sum-of-Products A sum-of-products expression is a product term (minterm) or several product terms (minterms) logically added (ORed) together. For example, the expression x-y + x-y is a sum-of-products expression. The following are all sum-of-products expressions: x x+y x+y•z x•y+z x•y+x•y•z The following steps are followed to express a Boolean function in its sum-of-products form: 1. Construct a truth table for the given Boolean function. 2. Form a minterm for each combination of the variables which produces a 1 in the function. 3. The desired expression is the sum (OR) of all the minterms obtained in step 2. For example, in case of function Fi of Figure 6.17, the following three combinations of the variables produce a 1: 001, 100, and 111 Their corresponding minterms are x-y-z, x-y-z, and x-y-z Hence, taking the sum (OR) of all these minterms, the function Fi can be expressed in its sum-of-products form as: F1 = x-y-z + x-y-z + x-y-z or F 2 = m , + m4 + m 7 Similarly, it may be easily verified that the function F 2 of Figure 6.17 can be expressed in its sum-of-products form as: F2 = x-y-z + x-y-z + x-y-z+x-y-z X y z 0 0 0 0 1 1 1 1 0 0 l I 0 0 1 1 0 1 0 1 0 1 0 1 or F2 = m3 + m5 + m6 + m7 F1 F2 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 Figure 6.17. Truth table for functions F1and F2. It is sometimes convenient to express a Boolean function in its sum-of-products form. If not in this form, it can...
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## This document was uploaded on 04/07/2014.

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