speciic Boolean algebra with just two elements 0 and 1 has been used in this chapter. Other Boolean algebras can be deined 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, deine each of the following for the new algebra so that the Boolean identities hold: