GROUP -A
1. Smart Elevator Control Logic
A smart elevator controller has 4 binary sensors:
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F: Floor requested (0 = even floor, 1 = odd floor)
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O: Overload sensor (0 = not overloaded, 1 = overloaded)
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D: Door open (0 = closed, 1 = open)
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E: Emergency button (0 = normal, 1 = emergency)
The elevator should start moving (output = 1) only under the following rules:
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It is not overloaded, and
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The door is closed, and
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Either:
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A valid floor request is made, or
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Emergency mode is activated
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Frame the minimized logic expression that controls movement.
🔹 2. Industrial Fan Safety System
In a chemical plant, a fan must be automatically turned ON when dangerous conditions arise.
Inputs:
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T = 1 if Temperature > 70°C
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G = 1 if Gas leakage is detected
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P = 1 if Power is available
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M = 1 if Manual override is enabled
The fan should turn on if:
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Either T or G is high, and P is available,
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Or if the manual override (M) is used (regardless of other inputs).
Design the minimized Boolean function to control the fan operation.
🔹 3. Smart Traffic Light Control (4-Way Intersection)
Sensors detect traffic at four roads (A, B, C, D) entering a junction.
Each sensor = 1 if traffic is detected, 0 otherwise.
A special green signal is triggered only if:
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At least three roads have traffic, and
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Road D has no traffic (priority to other directions).
Determine the minimal logic expression to control this special green signal.
🔹 4. Smart Irrigation Controller
Inputs:
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M = Moisture level low (1 = dry)
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R = Rain sensor (1 = rain)
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T = Timer condition met (1 = scheduled time)
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O = Operator override (1 = force on)
The irrigation pump must turn ON when:
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Moisture is low AND it is scheduled time,
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But NOT if rain is detected,
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Unless overridden by the operator.
Design and minimize the logic for the Pump ON signal.
🔹 5. Secure Access System – Restricted Logic
A door lock uses a 4-bit input (A, B, C, D) from a keypad. Only the following binary codes are valid to unlock the door:
0001, 0100, 1010, 1100, 1110, 1111
Other codes do not unlock the door.
Design the simplest logic function that outputs 1 for valid unlock attempts.
Also, use don't care conditions for 0000 and 1000, which are never generated.
🔹 6. Medical Device Alarm Logic
Inputs from sensors in a patient-monitoring device:
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H = Heart rate abnormal
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B = Blood pressure abnormal
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T = Temperature abnormal
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S = Sleep mode enabled
An alarm should activate only when:
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Any two or more vitals are abnormal, and
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Sleep mode is not enabled.
Write the Boolean function and minimize it to reduce logic hardware.
🔹 7. Data Transmission Fault Detection
A 4-bit checksum monitor system detects a fault when:
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The XOR of all bits is 1 (odd parity), and
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At least one bit is 1 (to ignore all-zero idle line)
Input bits: A, B, C, D
Design the logic for the Fault flag, and simplify the expression using grouping techniques.
GROUP -B
1. Complex Input Combinations (4 variables):
A digital security system uses four binary inputs A, B, C, and D. The output alarm is triggered (i.e., output = 1) for the following input states:
0, 2, 3, 6, 7, 8, 10, 11, 12, 13 (decimal values).
Additionally, the system designer notes that inputs 1 and 9 can never occur in practice.
Derive the most efficient logic expression to activate the alarm.
2. POS-type Minimization – Implied:
A logic function is 0 (false) for the input decimal values:
0, 1, 2, 5, 8, 9, 10, 14
For all other inputs (3, 4, 6, 7, 11, 12, 13, 15), the output is 1.
Find the minimized logic expression that defines this behavior.
3. Mixed Minterms with Don’t Care:
In a certain controller design, the output is 1 for the following binary combinations (decimal):
1, 3, 7, 11, 15
The combinations 0, 2, 5, 13 are considered irrelevant and may take either 0 or 1 (don’t care).
Find the most compact logic equation representing this output behavior.
4. Gray Code Sensitive System:
A system activates an output when the Gray code of a 3-bit input is one of the following:
000, 001, 011, 010 (in binary)
Determine the minimized Boolean expression for this output condition, using inputs A, B, and C where A is the MSB.
5. Pattern Recognition Function:
Design a logic function F(A, B, C, D) such that it outputs 1 only when the binary input represents a prime number less than 16 (i.e., 2, 3, 5, 7, 11, 13).
Derive the minimized Boolean expression to implement this logic.
6. Parity Detection with Conditions:
You have a 4-bit input (W, X, Y, Z).
The output should be 1 if the number of 1s in the input is odd, but only when W = 1.
Minimize the logic expression accordingly.
7. Unusual Grouped Logic Activation:
A logic circuit outputs high for inputs with the decimal values:
0, 1, 5, 7, 9, 11, 13, 15
Find the most efficient Boolean expression to represent this function.
Note: Direct SOP writing leads to long expressions; simplify optimally.
8. Dual Output Function Design:
Design two output functions F1 and F2 from 4 inputs A, B, C, D such that:
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F1 = 1 for minterms {0, 2, 5, 6, 8, 10, 13}
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F2 = 1 for maxterms {1, 4, 7, 9, 12, 14, 15}
Find minimal Boolean expressions for both functions, using any valid technique.
GROUP -C
1.
A digital circuit has three inputs A, B, and C. The output F is high (1) for the following input combinations:
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A=0, B=0, C=0
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A=0, B=1, C=0
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A=1, B=0, C=0
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A=1, B=1, C=0
Minimize the Boolean expression for F using a systematic approach.
2.
A function F(A, B, C) is true for input combinations corresponding to the decimal values 1, 3, 5, and 7.
Determine the simplest Boolean expression for F.
3.
A certain logic function outputs 1 for the binary inputs:
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0001
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0011
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0111
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1111
Assume the inputs are D, C, B, A (in that order). Derive the minimized expression for the output function.
4.
A circuit takes four inputs W, X, Y, Z and gives output 1 only for the decimal inputs 0, 2, 5, 7, 8, 10, 13, and 15.
Find the minimized Boolean expression for the output function.
5.
A digital system defines an output function that is high when the input is in the set {4, 5, 6, 7, 12, 13, 14, 15} and low otherwise.
Find the most simplified expression for this output.
6.
Given a truth table with inputs A, B, C, D, the output is 1 for the minterms:
(1, 3, 7, 11, 15).
Simplify the Boolean function using grouping techniques.
7.
A certain digital logic circuit uses three inputs A, B, and C. The output is high for all input combinations where the number of 1s in the input is even (including zero).
Determine the minimal logic expression for this output.
8.
A control signal is active (1) when the inputs (A, B, C, D) match the binary representations of the decimal values 2, 3, 6, 7, 10, 11, 14, 15.
Write the minimized Boolean expression for this control signal.
