📚 Lesson: Karnaugh Maps (K-Maps)
🎯 Learning Objectives
By the end of this lesson, students will be able to:
- Have basic knowledge about key combinational logic functions using standard ICs.
- Identify adders, decoders, multiplexers, and demultiplexers—building intuition from truth tables to practical ICs.
1️⃣ Adders: Half and Full
Half-Adder
Adds two bits:
- Sum (S) = A ⊕ B
- Carry (C) = A · B
| A | B | Sum (S) | Carry (C) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Full-Adder
Adds A + B + Carry-in (Ci):
- Sum (S) = A ⊕ B ⊕ Ci
- Carry-out (Co) = AB + Ci(A ⊕ B)
| Ci | A | B | Sum (S) | Carry-out (Co) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
MSI Example: 74HC283
- 4-bit full adder with fast carry
- Cascadable via carry-in/carry-out
- All bits use full-adder logic 📌 Use Ci = LOW to treat MSB as a half-adder
2️⃣ Decoders
Selects one output from many, based on the input code
74HC138: 3-to-8 Decoder
- Inputs: A0–A2
- Outputs: Y0–Y7 (active LOW)
- Enables: CS1 (active HIGH), CS2 & CS3 (active LOW)
Function: Selects one output based on 3-bit input.
| CS1 | CS2 | CS3 | A2 | A1 | A0 | Y0 | Y1 | Y2 | Y3 | Y4 | Y5 | Y6 | Y7 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| X | X | 1 | X | X | X | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| X | 1 | X | X | X | X | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | X | L | X | X | X | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
3️⃣ Multiplexer
- Connects only one of a number of possible inputs to a single output.++
74HC151: 8-to-1 Multiplexer
- Inputs: D0–D7
- Select: A0–A2
- Output: Y (non-inverted), Y̅ (inverted)
- Strobe: Active LOW Function: Routes one input to output based on select lines.
| A2 | A1 | A0 | Strobe | Y (non-inverted) | Y̅ (inverted) |
|---|---|---|---|---|---|
| X | X | X | H | L | H |
| 0 | 0 | 0 | L | D0 | D̅0 |
| 0 | 0 | 1 | L | D1 | D̅1 |
| 0 | 1 | 0 | L | D2 | D̅2 |
| 0 | 1 | 1 | L | D3 | D̅3 |
| 1 | 0 | 0 | L | D4 | D̅4 |
| 1 | 0 | 1 | L | D5 | D̅5 |
| 1 | 1 | 0 | L | D6 | D̅6 |
| 1 | 1 | 1 | L | D7 | D̅7 |
4️⃣ Demultiplexer
- It takes one input and connects it to one of a number of possible outputs
- The 74HC138 Decoder can also be used as a Demultiplexer.