1) Design a combinational circuit with three inputs, x, y and z, and three outputs, A, B, C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input. 2) A majority circuit is a combinational circuit whose output is equal to 1 if the input variables have more 1's than 0's. The output is 0 otherwise. Design a 3-input majority circuit by finding the circuit's truth table, Boolean equation, and a logic diagram. 3) Design a BCD-to-decimal decoder using the unused combinations of the BCD code as don't-care conditions. 4) Construct a 5-to-32-line decoder with four 3-to-8-line decoders with enable and a 2-to-4-line decoder. 5) Using a decoder and external gates, design the combinational circuits defined by the following five Boolean functions: a) F1 = x'yz' +xz b) F2 = (y' + x)Z c) F3 = xy'z' + x'y d) F4=y'z' + x'y + yz' e) F5 = x'y'z' + xy