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 circuit defined by the following three Boolean functions: a) F1=xyz+xz b) F1=(y+x)z c) F2=xyz+xy d) F2=yz+xy+yz e) F3=xyz+xy