9 a sum of products expression is a product term

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Unformatted text preview: + x (f) x-y = y-x (g) x + (y + z) = (x + y) + z (h)x(yz) = (xy)-z (i) x • (y + z) = x • y + x • z (j) x + y-z = (x + y)-(x + z) (k) x + x = 1 (1) x • x = 0 5. In Boolean algebra, there is a precise duality between the operators • (AND) and + (OR) and the digits 0 and 1. This property is known as the principle of duality. 6. The basic Boolean identities are summarized in Figure 6.12. They are very helpful while dealing with Boolean algebra. 7. A Boolean function is an expression formed with binary variables, the two binary operators OR and AND, the unary operator NOT, parentheses and equal sign. 8. The complement of a Boolean function F is F and is obtained by interchanging O's for l's and l's for O's in the truth table that defines the function. 9. 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. 10. A product-of-sums expression is a sum term (maxterm) or several sum terms (maxterms) logically multiplied (ANDed) together. For example, the expression (x + y) • (x + y) is a product of sums expression. 11. The sum-of-products and the product-of-sums form of Boolean expressions are known as standard forms. One prime reason for liking the sum-of-products or the product-of-sums expressions is their straightforward conversion to very nice gating networks. 12. A logic gate is an electronic circuit which operates on one or more input signals to produce standard output signals. These logic gates are the building blocks of all the circuits in a computer. 13. An AND gate is the physical realization of the logical multiplication (AND) operation. That is, it is an electronic circuit that generates an output signal of 1 only if all input signals are also 1. 14. An OR gate is the physical realization of the logical addition (OR) operation. That is, it is an electronic circuit that generates an output signal of 1 if any of the input signals is also 1. 15. A NOT gate is the physical realization of the complementation operati...
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