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# Using combination logic to determine the volume of a tank

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The volume of liquid in a fifteen-liter tank is measured to the nearest liter and presented in binary code to a combinational logic circuit represented by the block diagram in the attached figure. The output of the logic circuit represents the volume in pints.

Thus, for the input, DCBA = 0000 means the tank is empty and DCBA =1111 means the tank is full (15 liters). For the output, ZYXWV = 00000 implies an empty tank and ZYXWV = 111111 represents a reading of 31 pints.

a) Construct a truth table for the circuit.
b) Derive minimised boolean expressions for each output.
c) Design minimised circuits using direct logic (i.e. AND, OR and NOT gates only) for outputs Y and Z.
d) Design minimised circuits using just NAND gates for outputs Y and Z.

https://brainmass.com/computer-science/logic-design/using-combination-logic-to-determine-the-volume-of-a-tank-373669

#### Solution Preview

a) Though output ZYXWV is 5 bits and 11111 represents 31 pints; we never reach maximum value here as the maximum input is only 15 liters. Using standard conversion from liters to GB Pints, 1 liter = 1.76 pints, and rounding to nearest whole number we get the ...

#### Solution Summary

The volume of liquid in a fifteen-liter tank is measured to the nearest liter and presented in binary code to a combinational logic circuit represented by the block diagram in the attached figure. The output of the logic circuit represents the volume in pints.

Thus, for the input, DCBA = 0000 means the tank is empty and DCBA =1111 means the tank is full (15 liters). For the output, ZYXWV = 00000 implies an empty tank and ZYXWV = 111111 represents a reading of 31 pints.

a) Construct a truth table for the circuit.
b) Derive minimised boolean expressions for each output.
c) Design minimised circuits using direct logic (i.e. AND, OR and NOT gates only) for outputs Y and Z.
d) Design minimised circuits using just NAND gates for outputs Y and Z.

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## Help with a problem solving simulation is given.

This problem is assessed:

Consider this problem: A man has three animals on a riverbank: a dog,cat, and a mouse. The man needs to get all three animals to the other side of the river, but can only carry himself and one animal at a time.

The man cannot leave the dog and cat together because the dog will eat the cat. similarly, if the man leaves the cat and mouse together, the cat will eat the mouse.

Help the man figure out a system for transporting each of the animals across the river without any of them getting eaten.

Consider the following questions: Do you use a problem solving process?

*How did you interpret the problem?
*What strategy did you use and how did you evaluate your progress?
*Did you encounter any obstacles while solving the problem?
*Were you aware of this thought process as you worked through the problem?

I think you have to take the cat first. What do you think? I would really like some help.

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