# Using combination logic to determine the volume of a tank

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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#### 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.