Circuit Function: Decoder and Comparator for Lift Movement

This document explains the circuit function of a decoder and comparator for lift movement. It covers the working of a decoder to decode input values and a comparator to check for equality. The document includes circuit diagrams, a truth table, and additional requirements for accommodating more floors. It also discusses the conditions for lift movement.

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Circuit Function:
The circuit is a combinational circuit that can be built using basic Boolean gates. No memory
is required for the circuit functioning so it eliminates the need of any flip flops for circuit
design. The combination circuit part is built up using two sub components. A decoder and a
comparator.
Floor Decoder:
Decoder is a circuit that takes in n bits input and decodes it into one of the 2n outputs
depending upon value of the input given. Rest all outputs remain low. For the given
question, the input is a three bit value and hence will need a 3 to 8 decoder. However, not
all values are required for circuit and can be optimized. So only valid combinations are
decoded and given as a single bit output. Output being high means value entered for the
input is valid value else it remains 0.
The floor decoder takes the three bit input. It decodes them and gives a valid high output if
the value of input is one of the valid input values. i.e. 1, 2, 3, 5, 7 and stays 0 if input is 0, 4
or 6. The same unit is used twice, one for each input. Outputs from both units are checked
to be high. This would mean Present state of lift and destination of lift are both valid. This
fulfils the necessary condition for movement of lift from its current position.

Comparator:
Another unit is comparator. Function of comparator is to equate if two set of inputs are
equal. This is achieved using an EXOR gate function built using AND, OR and NOT gates. It
gives an output 1 if inputs are different else stay 0 in case both are equal. It takes in three
bit input and matches if both inputs are equal. If inputs are not equal it gives out a single bit
output as 1. This serves necessary condition that C must not be equal to D.
Combining these two outputs gives the final value whether the lift should move or not.

Circuit Diagrams:
C1-C3 is current state input of lift and D1-D3 is expected state of the lift after movement. Move Lift
signal turns high if both C and D are valid and different.

Truth Table:
C1 C2 C3 D1 D2 D3 Move
0 0 0 x x x 0
0 0 1 0 0 0 0
0 0 1 0 0 1 0
0 0 1 0 1 0 1
0 0 1 0 1 1 1
0 0 1 1 0 0 0
0 0 1 1 0 1 1
0 0 1 1 1 0 0
0 0 1 1 1 1 1
0 1 0 0 0 0 0
0 1 0 0 0 1 1
0 1 0 0 1 0 0
0 1 0 0 1 1 1
0 1 0 1 0 0 0
0 1 0 1 0 1 1
0 1 0 1 1 0 0
0 1 0 1 1 1 1
0 1 1 0 0 0 0
0 1 1 0 0 1 1
0 1 1 0 1 0 1
0 1 1 0 1 1 0
0 1 1 1 0 0 0
0 1 1 1 0 1 1
0 1 1 1 1 0 0
0 1 1 1 1 1 1
1 0 0 x x x 0
1 0 1 0 0 0 0
1 0 1 0 0 1 1
1 0 1 0 1 0 1
1 0 1 0 1 1 1
1 0 1 1 0 0 0
1 0 1 1 0 1 0
1 0 1 1 1 0 0
1 0 1 1 1 1 1
1 1 0 x x x 0
1 1 1 0 0 0 0
1 1 1 0 0 1 1
1 1 1 0 1 0 1
1 1 1 0 1 1 1
1 1 1 1 0 0 0
1 1 1 1 0 1 1
1 1 1 1 1 0 0
1 1 1 1 1 1 0

Additional Requirements:
i. Presently there are only 7 floors, so 3 bit value is sufficient to represent each
floor. In case when number of floor increases beyond 7, additional number of
bits will be required to represent floors. To accommodate more number of
floors, the number of bits required to represent the floors would need to
increase from 3 to 7. Increase in number of bits will need larger size of decoder
for decoding 7 bit inputs. As size of decoder increases, the number of AND gates
and inputs to AND gates will also increase. Each AND gate will now receive 7
inputs either in its direct form or in complement form to generate individual
minterm corresponding to each floor number.
To select valid value from decoder output, the invalid outputs will be tied to an
OR gate. Output of OR gate is inverted to indicate a valid value for C or D. Further
the size of comparator will also increase from 3 bits to 7 bits. Now more number
of Exor gate equivalents will be needed. Output of all such gates shall than be
ORed together to create a single bit Output. This output needs to be inverted to
indicate if both values are equal. Else it would remain low.
Output from Decoders and Comparators would proceed as before, when both
outputs are 0, it means lift can move from one floor to another. If either of them
is 1, it means one of the requirements is not satisfied and lift cannot move.
ii. When lift is allowed to make move from Private floor, it means present floor
value that is held in C is all valid. Any combination is now legal for lift to move
from one position to another. To make it legal for C to hold values corresponding
to Private floors, would mean all values on C are now valid, So no decoder would
be needed to check for C values. However Destination can still not be private
floor, so decoder will be needed to decode illegal values and generate a valid
signal for D values. Decode output for D will be needed to find out illegal floor
values. The output of decoder for D shall be a single bit value indicating a valid D
value. C is ignored as all values are valid.
Comparison for equality of D and C will be expanded to 7 bits. So both
conditions will generate a single bit output as before that can be ANDed to
indicate Lift movement.