Overview
This lecture explains how to implement Boolean functions using decoders and multiplexers, covering both normal and active-low types, and detailing practical connection steps.
Implementing Functions with Decoders
- A 3-to-8 decoder has 3 inputs (A, B, C) and 8 outputs, one for each possible input combination.
- Normal decoders output ‘1’ at the selected line, ‘0’ elsewhere.
- Active-low decoders output ‘0’ at the selected line, ‘1’ elsewhere; outputs are inverted (denoted by circles).
- To implement a function, connect the desired output lines (corresponding to minterms) to an OR gate for normal, or an AND gate for active-low decoders.
- In active-low decoders, a single ‘0’ output blocks the AND gate, resulting in correct function output logic.
Implementing Functions with Multiplexers
- A 4-to-1 multiplexer uses 2 select lines (B = most significant, C = least significant) and 1 output (F).
- The remaining input variable (A) is connected to the multiplexer data inputs according to a table:
- Top row: A' (A bar, or NOT A), lower values (0–3).
- Bottom row: A, higher values (4–7).
- For each column:
- Both rows circled: connect to 1.
- Only A row circled: connect to A.
- Only A' row circled: connect to A'.
- No circle: connect to 0.
- For functions of more than 3 variables, use 8-to-1 multiplexers and extend the selection bit logic.
Using Inverting Multiplexers
- Inverting multiplexers have a circle on the output; output is the inverse of normal operation.
- To implement a function, circle the ‘0’s in the function table instead of the ‘1’s.
- Row/column rules for connecting data inputs remain the same as the normal multiplexers.
Key Terms & Definitions
- Decoder — Combinational circuit that converts binary inputs to a one-hot output.
- Active-low Decoder — Decoder with inverted outputs; selected output is ‘0’.
- Multiplexer (MUX) — Device that selects one of several input signals and forwards it to a single output line.
- Select Lines — Control inputs that determine which data input is routed to the output.
- A bar (A’) — The NOT or inverse of input A.
Action Items / Next Steps
- Practice drawing and labeling decoders and multiplexers for given functions.
- Try implementing functions using both normal and active-low decoders.
- Complete exercises on constructing MUX input tables for various functions.