Using 5's complement, subtract (212)6 from (123)6 and represent the absolute value of the result using 84(2)(1) code. The (r1) s complement of a 2 digit number expressed in base r, when added to (15) 10 gives (67)10. If the sum and the difference of the two digits is (4)10 and (2)10, respectively, assuming the most significant digit is larger in magnitude, find the base r and express the number in base r. Design and implement a logic circuit to convert BCD to Excess- 3 code using only basic gates. Use K-Maps for simplification wherever necessary. Design and implement a logic circuit using only two level NOR gates to obtain the output as shown in the truth table (Table 1). (For two level implementation, assume the variables are available in their normal and complement forms.) Design an optimized gate level circuit, which will take 4 bit Gray input and display its corresponding HEX values uniquely in a common anode 7 segment display. Implement the function F(A,B,C,D,E,F)= (0,2,4,6,8,9,11,13,15,16,18,20,21,22,23,24,34,41,42,43,55,56,57,60) using a Multiplexer. (You may use one additional inverter, only, if required). Implement a 2 input XOR gate using a 4:1 Multiplexer. Inputs of the XOR gate are the select lines of the Multiplexer. You have 4 to 16 Decoder at your disposal. Using only that decoder, implement the following function: Y=4x, where X is a 4 bit input and Y is the output