FAQ
TL;DR: For the 3‑input truth table (8 rows), the minimal solutions are either one 4:1 MUX or a 5‑gate discrete design. “Multiplexors (aka Data Selectors) are powerful!” [Elektroda, Bob Loy, post #21664649]
Why it matters: This FAQ helps students and hobbyists choose the simplest, most reliable way to implement the specified logic with A, B, and C.
Quick Facts
- Lowest chip-count: single 4:1 MUX with selects B,C and data inputs A, A̅, A̅, 0. [Elektroda, Satyanarayana Murthy Kara, post #21664638]
- Minimized Boolean: y = A + A̅·B·C̅ → needs 2 NOT, 2 AND, 1 OR gate. [Elektroda, Syed Shadab, post #21664642]
- XOR-only fails: input 1,1,1 yields 1 instead of 0 with two cascaded XORs. [Elektroda, Bob Loy, post #21664649]
- K‑map approach is recommended for quick minimization and gate reduction. [Elektroda, Earl Albin, post #21664639]
- Sum-of-products version requires an OR stage to combine product terms. [Elektroda, Earl Albin, post #21664640]
What logic function matches this truth table?
A minimized expression is y = A + A̅·B·C̅. This implements the rows 001, 010, and 100 as 1, and all others as 0. It uses two inverters for A and C, two AND gates to build A̅·B·C̅, and one OR gate to combine with A. [Elektroda, Syed Shadab, post #21664642]
Can I build it with only two XOR gates?
No. Two XORs output 1 for A=B=C=1, but the table requires 0. This edge case breaks the XOR‑only idea. “Two XOR gates may not work.” Use the MUX or minimized SOP instead. [Elektroda, Bob Loy, post #21664649]
What’s the lowest chip‑count way to implement it?
Use one 4:1 multiplexer. Tie the select lines to B and C. Feed data inputs as D0=A, D1=A̅, D2=A̅, D3=0. This maps the rows to the required outputs with minimal wiring and one package. [Elektroda, Satyanarayana Murthy Kara, post #21664638]
How do I minimize it with a Karnaugh map?
Three steps: 1) Plot 1s at 001, 010, 100. 2) Group cells to cover those minterms with largest implicants. 3) Read groups to get y = A + A̅·B·C̅. K‑maps quickly show minimal terms for three inputs. [Elektroda, Earl Albin, post #21664639]
How many discrete gates do I need for the SOP build?
Five total: 2 NOT gates (invert A and C), 2 AND gates (build A̅·B·C̅), and 1 OR gate to produce y. This is compact and easy to wire on a breadboard. [Elektroda, Syed Shadab, post #21664642]
Do I need an OR gate after the AND terms?
Yes. Sum‑of‑products requires an OR stage to combine product terms into the final output. Use a 3‑input OR if you expand terms, or 2‑input OR for the minimized form shown. [Elektroda, Earl Albin, post #21664640]
How could a single toggle switch be used here?
Use it as a clock. Drive a 3‑bit counter through 0–7, then decode with a MUX or minimized logic to show the output for each state. The switch alone can’t replace three independent inputs. [Elektroda, Mark Harrington, post #21664651]
Why might a microcontroller be a better choice?
A small MCU can implement the truth table as a lookup with three GPIOs, reducing parts and enabling quick changes. One chip replaces multiple gates, improving reuse and flexibility. [Elektroda, Mark Harrington, post #21664643]
Is the 4:1 MUX approach really that good?
Yes. It yields low wiring and a single IC. As one expert said, “Multiplexors (aka Data Selectors) are powerful!” For this table, the MUX mapping is direct and clean. [Elektroda, Bob Loy, post #21664649]
What Mac software can I use to draw the circuit?
Try LogicCircuit for schematic simulation and learning. The thread notes it and queries Mac availability. If unavailable, use any cross‑platform simulator you prefer. [Elektroda, Mark Harrington, post #21664643]
What goes wrong in the XOR chain at A=B=C=1?
First XOR of A and B outputs 0. The second XOR then passes C as 1, giving y=1. The required output is 0, so XOR fails on 111. [Elektroda, Bob Loy, post #21664649]
Can one switch select among A, B, and C as inputs and still meet the table?
Not by itself. A single selector can’t emulate three independent Boolean inputs. Use the counter‑plus‑decoder idea to step states, or keep three separate inputs. [Elektroda, Bob Loy, post #21664653]
