ELEC2141: Digital Circuit Design – Magnitude Comparator – Combinational Circuit Assessment Answer

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Code: ELEC2141
Digital Circuit Design Assessment Answer
Assignment Task:
Question 1
Design a combinational circuit that controls an automated water sprinkler system. The inputs to the system include:

MORN
: a 1-bit signal that becomes 1 between 7:00 and 7:30 AM and is 0 otherwise.

EVEN
: a 1-bit signal that becomes 1 between 6:00 and 6:30 PM and is 0 otherwise.

RAIN
: a 1-bit signal that is 1 when it is raining and 0 otherwise.

HUMID
: a 2-bit signal that indicates the level of humidity in the air according to the following encoding:

Very humid 01: Humid 10: Dry 11: Very dry

SALINE
: a 1-bit signal that becomes 0 when the soil salinity level becomes too high and is 1 otherwise.

DRY
: a 1-bit signal that becomes 1 when the soil is too dry and is 0 otherwise.

EMPTY
: a 1-bit signal that becomes 0 when the water level in the reservoir supplying the sprinklers is too low and is 1 otherwise.

The system has three mutually-exclusive operation modes:

STANDBY
: normal
OFF
condition; water is not flowing.

PUMPING
: normal
ON
condition; water is flowing.

ALARM
: abnormal
OFF
condition; water should be flowing but is not because the water level in the reservoir is too low.

The normal
ON
condition should occur twice a day (when either
MORN
or
EVEN
are true) unless it is raining. The
ON
condition is also activated whenever both the soil salinity and dryness levels become too high. When in the
PUMPING
mode, the water flow rate depends on the air humidity and soil conditions as per:

Soil Air Flow Rate
Dry and saline – Very High Neither dry nor saline Very dry High Neither dry nor saline Dry Normal Neither dry nor saline Humid Low Neither dry nor saline Very humid Very low Dry and not saline – Normal Not dry but saline – Low
The system has these outputs:

PUMP
: a 1-bit signal that turns the pump on so water flows through the sprinklers

FLOW
: a 3-bit signal that controls the water flow rate

SEVEN
: a 7-bit signal used to indicate the operation mode on a 7-segment display. The letter S on the display indicates
STANDBY
, P indicates
PUMPING
and A indicates
ALARM
.

Question 2
A magnitude comparator is used to determine the relative magnitude of two binary numbers, with applications in numerous digital systems. In general, a comparator performs a magnitude comparison of two binary numbers A and B and provides three outputs, A B. Comparators are available in IC form with different bit comparing configurations, e.g. 4-bit, 8-bit. More than one comparator can also be connected in cascade arrangement to perform comparison of numbers of longer lengths.
To compare the two binary numbers, first the most significant bits (MSBs) are compared. If the MSBs are equal, then the next significant bits are compared. However, if the MSBs are not equal, then either A is greater than or less than B hence further comparison is not needed. For example, when comparing two 2-bit numbers given by A=A
Q
A and B=B
Q
B . If A
Q
? B
Q
, then A>B if A
Q
= 1, B
Q
= 0 or A B. The comparator overall generates three outputs, L, E and G, corresponding to whether A < B, A = B, A>B.
Design a comparator that compares two 4-bit binary numbers. Use multiple 4-bit comparators to design a system that compares three 4-bit binary numbers considering what the possible outputs of a three number comparator would be.
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