Name EE CE 3320 Dr Amir Khoobroo Exam 1 Review Problem 1 Assume that 0 V is encoded as 00 1 V as 01 2 V as 10 and 3 V as 11 You are given a digital encoding of an audio signal as follows 1001101101101011 Plot the re created signal with time on the x axis and voltage on the y axis Assume that each encoding s corresponding voltage should be output for 1 millisecond Problem 2 Convert the following binary numbers to decimal numbers Show your Work 1 101101 2 0101000100101 3 31 4 526 Problem 3 1 BA 2 E4C8 3 11110001 4 0101101011 Convert the following decimal numbers to binary numbers Show your Work a Convert the following hexadecimal numbers to binary Show your Work b Convert the following binary numbers to hexadecimal Show your Work Problem 4 Suppose a banking system supports encrypted transactions and that decrypting each transaction consists of three sub tasks A B and C The execution times of each task on a microprocessor versus a custom digital circuit are 5ms versus 1ms for A 10ms versus 2ms for B and 2ms versus 1ms for C Partition the tasks among the microprocessor and custom digital circuitry such that you minimize the amount of custom digital circuitry while meeting the constraint of decrypting at least 50 transactions per second Assume each task requires the same amount of digital circuitry Problem 5 Convert each of the following equations directly to gate level circuits a F ab c a bc b F a b c d e f g Problem 6 Determine whether the Boolean functions F ab and G a ab are equivalent using a algebraic manipulation and b truth tables Problem 7 Create a 4 bit prime number detector The circuit has four inputs N3 N2 N1 and N0 that correspond to a 4 bit number N3 is the most significant bit and one output P that is 1 when the input is a prime number and that is 0 otherwise Note 1 is not a prime number Problem 8 A house has four external doors each with a sensor that outputs 1 if its door is open Inside the house is a single LED that a homeowner wishes to use to indicate whether a door is open or closed Because the LED can only show the status of one sensor the homeowner buys a switch that can be set to 0 1 2 or 3 and that has a 2 bit output representing the switch position in binary Create a circuit to connect the four sensors the switch and the LED Use Gates Mux Decoder as needed Problem 9 Perform two level logic size optimization for F a b c d abc d ab cd Assuming that a and b can never both be 0 at the same time and that c and d can never both be 1 at the same time i e there are don t cares Problem 10 Compare the behavior of D latch and D flip flop devices by completing the timing diagram shown below Provide a brief explanation of the behavior of each device Assume each device initially stores a 1 Q Latch Q FF