You are asked to design a 4-to-3 parity counter. Such a circuit has 4 input bits,...

 

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You are asked to design a 4-to-3 parity counter. Such a circuit has 4 input bits, A, B, C, D and 3 output bits F2, F1, Fo. The value that the circuit outputs is the number of its input bits that are set to 1. For example if the input is 1010, then the circuit will output 010 (which is the binary representation of 2 as the unsigned 3-digit binary number FF1Fo). Similarly, if the input is 1111, then the output will be 100. Consider F2 as the highest order bit of the result and Fo as the lowest order bit. i. Construct the truth table for this circuit. ii. Write down the Boolean expressions for each of the three outputs in sum of products form. Now, simplify each expression using the laws of Boolean algebra to derive minimized sum-of-products forms. iii. Design this circuit in Logisim and test it. The TAs should be able to change the logical values of the inputs while obtaining the correct output. You are asked to design a 4-to-3 parity counter. Such a circuit has 4 input bits, A, B, C, D and 3 output bits F2, F1, Fo. The value that the circuit outputs is the number of its input bits that are set to 1. For example if the input is 1010, then the circuit will output 010 (which is the binary representation of 2 as the unsigned 3-digit binary number FF1Fo). Similarly, if the input is 1111, then the output will be 100. Consider F2 as the highest order bit of the result and Fo as the lowest order bit. i. Construct the truth table for this circuit. ii. Write down the Boolean expressions for each of the three outputs in sum of products form. Now, simplify each expression using the laws of Boolean algebra to derive minimized sum-of-products forms. iii. Design this circuit in Logisim and test it. The TAs should be able to change the logical values of the inputs while obtaining the correct output.