Give the 8-bit twos complement representations of the

Question

1. Give the 8-bit two's complement representations of the following integers: 55, 83, -79, -88.
2. Give the integer (in standard base-10 notation) which is represented by each of the following 8-bit two's complement numbers: 10000000, 11110011, 11111111.
3. Compute the following using 8-bit two's complement representations, as shown in class and described in the text: -79 + 55, -79 - 88, and 83 + 55. In each case, indicate whether the calculation results in an overflow. If it does not result in an overflow, then verify that your answer is correct by converting the result back to standard base-10 notation. Note: Use the two's complement representations from part i above.
4. What range of numbers can be represented in (a) 10-bit two's complement? What are the minimum number of bits necessary to represent (b) 2015 and (c) -99 in two's complement?
5. What is the maximum number of bits that may be needed to represent the multiplication of a 6-bit number with a 8-bit number? Justify your answer.

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 C0 such that C1 and C0 corresponds to the index (0 to 3) of the most significant input bit. Forexample,forinputA3=0,A2=1,A1=0,A0=1,thedesiredoutputofF isC1 =1and C0 = 0 which corresponds to the index 2. Also, assume that if the input binary number is 0000, then the output is 00.

1. Construct the truth table for the above circuit. Note that F has four input bits and two output bits.
2. Using the CNF construction by 0s, construct a Boolean formula for the output bit C1.
3. 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.
4. Using the CNF construction by 0s, construct the Boolean formula for the output bit C0.
5. 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.
6. Using your answers for the above parts, build a circuit for F using the simplified boolean functions.
7. (Bonus Question) The circuit descibed above is a simplified version of a circuitary that is used to implement a priority fuction. What is the name of this circuit.