The plus (+) indicates a more advanced problem and the asterisk (*) indicates that a solut...

The plus (+) indicates a more advanced problem and the asterisk (*) indicates that a solution is available on the Companion Website for the text.

+A specific Boolean algebra with just two elements 0 and 1 has been used in this chapter. Other Boolean algebras can be defined with more than two elements by using elements that correspond to binary strings. These algebras form the mathematical foundation for bitwise logical operations that we will study in Chapter 6. Suppose that the strings are each a nibble (half of a byte) of four bits. Then there are 24, or 16, elements in the algebra, where an element I is the four-bit nibble in binary corresponding to I in decimal. Based on bitwise application of the two-element Boolean algebra, define each of the following for the new algebra so that the Boolean identities hold:

(a) The OR operation A + B for any two elements A and B

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(b) The AND operation A ∙ B for any two elements A and B

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(c) The element that acts as the 0 for the algebra

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(d) The element that acts as the 1 for the algebra

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(e) For any element A, the element .