Explain in detail

1. [5 points] Design a combinational circuit whose input is a 5-bit number and whose output is the number of ones in the input. For example, the 5 -bit number 10010 base-2 has two ones. Maximum number of ones in the input is five and minimum is zero. Complete tasks P,Q, and R (see below) for this exercise. [5 points] Suppose that a combinational circuit is to be designed to control the Low-Fuel Indicator (LFI) light of a car. If the car's fuel levels are too low the LFI turns on, otherwise the LFI stays off. The car's fuel tank has a sensor attached to it that outputs the amount of fuel in the tank as a 4bit number. So if the sensor's output is 0000 base-2 it means there are 0 base- 10 liters of fuel in the tank, if the sensor's output is 1100 base-2 then it means there are 12 base-10 liters of fuel in the tank. The amount of fuel in the tank is always measured in liters and always an integer number i.e. minimum amount of fuel in the tank would be 0 base-10 liters and maximum amount of fuel in the tank would be 15 base-10 liters and all integers in between 0 and 15 could be the amount of fuel left in the tank. LFI turns on if fuel level in the tank of the car is below 5 base-10 liters, otherwise the LFI stays off. Complete tasks P,Q, and R (see below) for this exercise. P. Formulation a. Design the truth table b. Convert the truth table into a Boolean expression in standard sum of product form c. Measure the cost of your circuit by analyzing the Boolean expression and writing down the following costs i. Literal cost ii. Gate-input cost iii. Not gate cost iv. total Q. Optimization a. For each output bit of your truth table i. form an appropriate KMap with the correct minterms containing ones ii. Optimize the KMap in SOP form 1. Highlight essential prime implicants, non-essential prime implicants iii. Write the final Boolean expression in SOP form iv. Measure the cost of your circuit by analyzing the optimized Boolean expression and writing down the following costs 1. Literal cost 2. Gate-input cost 3. Not gate cost 4. Total R. Technology Mapping a. Please check document on Canvas > Modules Resources titled CircuitDesignSoftware.docx for software you may want to use to design your circuit with. b. For each of the optimized Boolean expressions from previous step i. Draw the circuit using AND, OR, and NOT gates. You should use software such as LogicWorks or Logisim to draw the circuit as this software will be useful in the next task. 1. Take a snapshot of your circuit and paste inside this document ii. Redraw the circuit using only NOR gates. You should use software such as LogicWorks or Logisim to draw the circuit as this software will be useful in the next task. 1. Take a snapshot of your circuit and paste inside this document