and 3 outputs (Output 1, Output 2, and Output 3). A C D 0 0 0...

   
 
 

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and 3 outputs (Output 1, Output 2, and Output 3). A C D 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 Below is a truth table with 4 inputs (A,B,C, and D) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Output 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 Output 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 Output 3 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 A) [3 marks] Define a set of statements, using Boolean logic, that satisfy the truth table above. Since there are three outputs in the truth table, you should create three logical statements. Make sure you show *how* you arrived at the statements by listing the rows and columns in the table that led you to choose a Boolean operator. B) [3 marks] Draw the circuit that corresponds to your logical statements. You may use a drawing tool if you like or you can use pencil and paper. (ensure your writing is dark enough to easily read in the scan or screenshot provided). Question 3: [6 Total] An Arithmetic Logic Unit is an integrated circuit that can perform several different arithmetic operations. The desired operation is selected using a binary code. In this question, you will design a very simple ALU. It only works on two 1-bit numbers, and it can perform either addition or multiplication. There are three inputs: two binary digits x and y, and one bit q to choose the operation. q = 0 selects multiplication and q = 1 selects addition. There are two outputs: z, the one-bit result of the chosen operation, and s, a status code. If addition is chosen, then s is the carry digit. If multiplication is chosen, then s = 0. This question can be answered with a single circuit diagram. No explanations are required. a) [2 marks] Fill in boxes A1 and A2 with logic gates so that the output of A1 is the one-bit sum X + Y and the output of A2 is the one-bit product X * Y. Use exactly one logic gate in each box. X I Y A1 A2 x + y x y b) [2 marks] Next, fill in the boxes B1 and B2 with logic gates as follows. The output of B1 is x +y if q = 1, and 0 if q = 0. The output of B2 is x * y if q = 0, and 0 if q = 1. For B1, use exactly one logic gate. For B2, use exactly two logic gates. It might be useful to write out the truth tables for the outputs of B1 and B2, using q and the outputs of A1 and A2 as inputs. q A1 19 A2 Y B1 B2 B1 output B2 output c) [1 mark] Now fill in the box C1 with exactly one logic gate so that the output of C1 is z, the outcome of the desired calculation. That is, z = x + y if q = 1, and z = x * y if q = 0. Again, a truth table for C1 might be helpful, using the outputs of B1 and B2 as inputs. q T Y A1 A2 B1 B2 C1 d) [1 mark] Finally, add exactly one more logic gate to your diagram so that its output is s, the status code. That is, s is the carry digit of x+y if q = 1, and s = 0 if q = 0. You will have to decide what the inputs of this last gate should be. and 3 outputs (Output 1, Output 2, and Output 3). A C D 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 Below is a truth table with 4 inputs (A,B,C, and D) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 Output 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 Output 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 Output 3 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 A) [3 marks] Define a set of statements, using Boolean logic, that satisfy the truth table above. Since there are three outputs in the truth table, you should create three logical statements. Make sure you show *how* you arrived at the statements by listing the rows and columns in the table that led you to choose a Boolean operator. B) [3 marks] Draw the circuit that corresponds to your logical statements. You may use a drawing tool if you like or you can use pencil and paper. (ensure your writing is dark enough to easily read in the scan or screenshot provided). Question 3: [6 Total] An Arithmetic Logic Unit is an integrated circuit that can perform several different arithmetic operations. The desired operation is selected using a binary code. In this question, you will design a very simple ALU. It only works on two 1-bit numbers, and it can perform either addition or multiplication. There are three inputs: two binary digits x and y, and one bit q to choose the operation. q = 0 selects multiplication and q = 1 selects addition. There are two outputs: z, the one-bit result of the chosen operation, and s, a status code. If addition is chosen, then s is the carry digit. If multiplication is chosen, then s = 0. This question can be answered with a single circuit diagram. No explanations are required. a) [2 marks] Fill in boxes A1 and A2 with logic gates so that the output of A1 is the one-bit sum X + Y and the output of A2 is the one-bit product X * Y. Use exactly one logic gate in each box. X I Y A1 A2 x + y x y b) [2 marks] Next, fill in the boxes B1 and B2 with logic gates as follows. The output of B1 is x +y if q = 1, and 0 if q = 0. The output of B2 is x * y if q = 0, and 0 if q = 1. For B1, use exactly one logic gate. For B2, use exactly two logic gates. It might be useful to write out the truth tables for the outputs of B1 and B2, using q and the outputs of A1 and A2 as inputs. q A1 19 A2 Y B1 B2 B1 output B2 output c) [1 mark] Now fill in the box C1 with exactly one logic gate so that the output of C1 is z, the outcome of the desired calculation. That is, z = x + y if q = 1, and z = x * y if q = 0. Again, a truth table for C1 might be helpful, using the outputs of B1 and B2 as inputs. q T Y A1 A2 B1 B2 C1 d) [1 mark] Finally, add exactly one more logic gate to your diagram so that its output is s, the status code. That is, s is the carry digit of x+y if q = 1, and s = 0 if q = 0. You will have to decide what the inputs of this last gate should be.