Design a combinational circuit F that receives four input signals and outputs 2 output signals. F...

 

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Design a combinational circuit F that receives four input signals and outputs 2 output signals. F takes as input four bits labeled A3, A2, A1, A0 and returns as output a two bit number labeled C₁ and Co such that C₁ and Co corresponds to the index (0 to 3) of the most significant input bit. For example, for input A3 = 0, A2 = 1, A1 = 0, A0 = 1, the desired output of F is C₁ = 1 and Co = 0 which corresponds to the index 2. Also, assume that if the input binary number is 0000, then the output is 00. i. Construct the truth table for the above circuit. Note that F has four input bits and two output bits. ii. Using the CNF construction by Os, construct a Boolean formula for the output bit C₁. iii. Using the Laws of Logic, simplify your Boolean formula from part (ii). Make your final formula as small as you can, in terms of the total number of variables and operators in the formula. iv. Using the CNF construction by Os, construct the Boolean formula for the output bit Co. v. Using the Laws of Logic, simplify your Boolean formula from part (iv). Make your final formula as small as you can, in terms of the total number of variables and operators in the formula. vi. Using your answers for the above parts, build a circuit for F using the boolean simplified functions. vii. (Bonus Question) This circuit is a simplified version of a circuitary that is used to form part of the vector address by implementing a priority fuction. What the name of this circuit. Design a combinational circuit F that receives four input signals and outputs 2 output signals. F takes as input four bits labeled A3, A2, A1, A0 and returns as output a two bit number labeled C₁ and Co such that C₁ and Co corresponds to the index (0 to 3) of the most significant input bit. For example, for input A3 = 0, A2 = 1, A1 = 0, A0 = 1, the desired output of F is C₁ = 1 and Co = 0 which corresponds to the index 2. Also, assume that if the input binary number is 0000, then the output is 00. i. Construct the truth table for the above circuit. Note that F has four input bits and two output bits. ii. Using the CNF construction by Os, construct a Boolean formula for the output bit C₁. iii. Using the Laws of Logic, simplify your Boolean formula from part (ii). Make your final formula as small as you can, in terms of the total number of variables and operators in the formula. iv. Using the CNF construction by Os, construct the Boolean formula for the output bit Co. v. Using the Laws of Logic, simplify your Boolean formula from part (iv). Make your final formula as small as you can, in terms of the total number of variables and operators in the formula. vi. Using your answers for the above parts, build a circuit for F using the boolean simplified functions. vii. (Bonus Question) This circuit is a simplified version of a circuitary that is used to form part of the vector address by implementing a priority fuction. What the name of this circuit.

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Lets design a combinational circuit F that takes four input signals A3 A2 A1 A0 and outputs two bits ... View the full answer