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Please Do Part :

A4 , A5 , A6

7.14 Exercises Because this interactive zy Book version may have been re-ordered and hence sections renumbered, section numbers below labeled with COD refer to the original hardcopy book's section numbers. A.1 (10] In addition to the basic laws we discussed in this section, there are two important theorems, called De Morgan's theorems: A+B= A.Band A.B= A + B Prove DeMorgan's theorems with a truth table of the form A B A B A.B 0 0 0 1 0 1 1 1 0 A+B 1 0 A.B 1 0 1 1 A+B 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 A.2 (15) Prove that the two equations for E are equivalent by using DeMorgan's theorems and the axioms shown COD Section A.2 (Gates, truth tables, and logical equations). E =((A.B)+(A.C) +(B-C)). (A.B.C) E = (A.B.C)+(A.C.B)+(B.C.A) A.3 [10] Show that there are 2 entries in a truth table for a function with n inputs. A.4 [10] One logic function that is used for a variety of purposes (including within adders and to compute parity) is exclusive OR. The output of a two-input exclusive OR function is true only if exactly one of the inputs is true. Show the truth table for a two-input exclusive OR function and implement this function using AND gates, OR gates, and inverters. A.5 [15] Prove that the NOR gate is universal by showing how to build the AND, OR, and NOT functions using a two-input NOR gate. A.6 [15] Prove that the NAND gate is universal by showing how to build the AND, OR, and NOT functions using a two-input NAND gate