Detailed Notes on Digital Design: Comparators, Decoders, and Encoders
1-Bit Comparator
- Outputs: 3 Types of Output:
- Truth Table for 1-bit:
- A < B is represented as A'B
- A = B is represented as A'B' + AB = A ⊕ B
- A > B is represented as AB'
2-Bit Comparator
- Inputs: Two 2-bit numbers (A1 A0 and B1 B0)
- Outputs: 3 Outputs similar to 1-bit comparator
- Truth Table: All possible combinations of A and B states result in outputs A < B, A = B, and A > B.
- Evaluation: Similar logical operations used as in the 1-bit case but applied to two bits each.
4-Bit Comparator
- Inputs: Two 4-bit numbers (A3 A2 A1 A0 and B3 B2 B1 B0)
- General Rules:
- A > B if:
- A3 = 1 and B3 = 0
- A3 = B3 and A2 = 1 and B2 = 0
- A3 = B3, A2 = B2 and A1 = 1 and B1 = 0
- A3 = B3, A2 = B2, A1 = B1 and A0 = 1 and B0 = 0
Boolean Expressions for Comparators
- A > B: A1B1' + A0B1'B0' + A1A0B0'
- A = B: A1'A0'B1'B0' + A1'A0B1B0 + A1A0B1B0 + A1A0'B1B0'
- A < B: A1'B1 + A0'B1B0 + A1'A0'B0
Decoders
- Functionality: For a given input combination, 1 output activates.
- Logic: n inputs yield 2^n outputs (e.g. 1 to 2, 2 to 4, 3 to 8, etc.)
- Components: Examples include 74xx146 (3-8 decoder), 74xx4514 (4-16 decoder)
Active High vs. Active Low Logic
- Active High: Logic levels defined as ON = 1
- Active Low: Logic levels defined as ON = 0
- Example: The chip being discussed is active low.
Encoders
- Overview: Function as the reverse of decoders, where 2^n inputs yield n outputs.
- Common Models: 74xx148 (8-3 encoder), 74xx147 (10-4 encoder)
Applications of Comparators, Decoders, and Encoders
- Comparators: Used in sensors (such as temperature or position), motor control systems, and password verification.
- Decoders: Memory addressing, and controlling functionalities in devices (like switching between a TV and projector screen).
- Encoders: Useful in keypads where encoded output is easier to transmit.
Additional Notes
- The following chapters to be explored in upcoming lectures include multiplexers, demultiplexers, and parity generators/checkers.