Related Concepts: 5.01 Arithmetic Circuits, Multipliers & Comparators | 5.02 Code Converters & Data Routing Implementations | 5.04 Programmable Logic Devices (ROM & PLA)

5.05 Application-Specific Word Problems

Real-World Logic Synthesis

Application-specific word problems test your ability to convert a real-world scenario into formal Boolean expressions: defining input/output variables $\to$ constructing the truth table $\to$ simplifying via K-map $\to$ drawing the hardware circuit.

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1. The Restaurant Voting Tie-Breaker Logic

Major PYQ Problem (2016 - 11 Marks)

Scenario: Mom ($A$), Dad ($B$), Joe ($C$), Sue ($D$) vote: Vegetables ($1$) vs. Chicken ($0$). Rules:

1. Majority vote wins.
2. If Mom and Dad agree, they win regardless of the kids.
3. Any other tie votes result in Chicken ($0$).

Solution:

• Minterms where $Y=1$: $Y=\Sigma m(7,11,12,13,14,15)$
• K-map simplification:
  • Quad $(12,13,14,15)\to AB$ (Mom & Dad agree)
  • Pair $(7,15)\to BCD$
  • Pair $(11,15)\to ACD$ $\mathbf{Y}=\mathbf{AB}+\mathbf{ACD}+\mathbf{BCD}=\mathbf{AB}+\mathbf{CD}(\mathbf{A}+\mathbf{B})■$

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2. The Spaceship Battery Monitor

Major PYQ Problem (2017 - 13 Marks)

Scenario: A 4-bit A/D converter ($A,B,C,D$) monitors a 0-15V battery. Generate HIGH output if voltage $>6\text{V}$.

Solution:

• Minterms for $>6\text{V}$: $Y=\Sigma m(7,8,9,10,11,12,13,14,15)$
• K-map simplification: Octet $(8\dots 15)\to A$, Pair $(7,15)\to BCD$. $\mathbf{Y}=\mathbf{A}+\mathbf{BCD}■$

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3. Gas-Fired Boiler Alarm System

Major PYQ Problem (2021 - 10 Marks)

Scenario: Flame ($F$), Chimney Temp ($C$), Water Temp ($W$), Pressure ($P$). Alarm triggers if flame ignited AND chimney temp OR water temp OR pressure is high.

$\text{Alarm}=\mathbf{F}\cdot (\mathbf{C}+\mathbf{W}+\mathbf{P})■$

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4. 4-Bit Divisibility Indicator (Divisible by 2 and 3)

Major PYQ Problem (2022 - 8 Marks)

Scenario: 4-bit input ($A,B,C,D$). Output $Z_1=1$ if divisible by 2; $Z_2=1$ if divisible by 3.

Solution:

• Divisible by 2 ($Z_1$): LSB must be $0⟹{\mathbf{Z}}_1={\mathbf{D}}^{\prime }$
• Divisible by 3 ($Z_2$): Numbers $0,3,6,9,12,15⟹Z_2=\sum m(0,3,6,9,12,15)$ ${\mathbf{Z}}_2=(\mathbf{A}\odot \mathbf{B})(\mathbf{C}\odot \mathbf{D})+{\mathbf{A}}^{\prime }\mathbf{BC}{\mathbf{D}}^{\prime }+\mathbf{A}{\mathbf{B}}^{\prime }{\mathbf{C}}^{\prime }\mathbf{D}■$

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Past Year Questions (PYQs)

Question (as asked)	Years	Marks	Solved in
Restaurant voting logic — majority wins, except Mom and Dad agreeing overrides; other ties go to chicken	2016	11	§Restaurant
Spaceship battery monitor — output indicates whether the analog voltage exceeds 6 V	2017	13	§Spaceship
Gas-fired boiler alarm — alarm when the burner flame is ignited and chimney temperature or water temperature or boiler pressure is high	2021	10	§Boiler
4-bit divisibility indicator — $z_1$ for divisible by 2, $z_2$ for divisible by 3	2022	8	§Divisibility

Pattern to notice: a word problem appears in roughly every other paper for 8–13 marks, and the scenario is different every single time — there is nothing to memorise. What transfers is the five-step blueprint in 5.01 Arithmetic Circuits, Multipliers & Comparators §1: identify variables → truth table → K-map per output → minimised equations → schematic.

Where the marks actually sit: almost entirely in translating the English into a correct truth table. Read the wording twice and pin down the ambiguities before writing anything — in the 2016 restaurant problem, “the majority wins, except Mom and Dad agree, and in that case they win” is a priority override that changes four rows. Getting the table right and then doing a slightly clumsy K-map still scores well; a beautiful K-map on a wrong table scores almost nothing.

Watch for impossible input states — they become don’t cares and usually simplify the answer considerably.