Lecture 8: MSI Components

Lecture 8: MSI Components

• The lecture covered decoders, encoders, multiplexers, and demultiplexers as MSI components.
• Decoders: Implement functions using decoders, decoder with enable, and standard MSI decoder.
• Encoders: Priority encoders.
• Multiplexers: Standard MSI multiplexer, implementing functions using multiplexers, and using smaller multiplexers.

Decoders

• Decoders translate a coded input into a specific output.
• A decoder takes an input code and activates a corresponding output line.
• Each output corresponds to a unique input code.
• Decoders are useful for selecting a specific output based on the input code.
• Illustrative example: if codes 00, 01, 10, and 11 are used to identify four persons, a 2-bit decoder can be used.

Decoding (Inefficient vs Efficient Way)

• Inefficient decoding: Sequential checking of each possible code to identify the target entity.
• Efficient decoding: Using a decoder to directly identify the target entity based on its code.

Decoders (2/5)

• Example: A 2x4 decoder selects an output line based on a 2-bit code.
• A 2x4 decoder has two input lines (X, Y) and four output lines (F0, F1, F2, F3).
• The truth table shows the output lines activated based on the input code.

Decoders (3/5)

• From the truth table, a circuit diagram depicts the logic for a 2x4 decoder.
• Each output represents a minterm in a 2-variable function.
• The circuit diagram defines the relationship between inputs and outputs.

Decoders (4/5)

• Designing a 3x8 decoder involves a truth table mapping input (x,y,z) to outputs (F0,F1,…,F7)
• Each output corresponds to a specific minterm of a 3-variable Boolean function.

Decoders (1/3): Implementing Functions

• Decoding in sum-of-minterms form, implemented with a decoder and OR gates
• Combinational circuits with n-inputs and m-outputs are implemented using an n:2^n decoder and m OR gates.
• Useful when a circuit with many outputs is efficiently expressed using few minterms.

Decoders (2/3): Example - Full Adder

• Illustration with 3x8 decoders for a full adder function, mapping inputs and outputs.

Decoders (3/3): Example and more detail illustration

• Detailed circuit implementation of a 3x8 decoder.
• Illustrative example of a 3x8 decoder used in the implementation of a full adder.

Decoders with Enable (1/2)

• Decoders often include an enable signal (E) to control the activation of the device.
• The decoder operates only when E=1.
• Outputs F0 to F3 are dependent on the values of input lines X and Y along with the active enable signal.

Decoders with Enable (2/2)

• Enabling signals are generally zero-enabled, meaning the decoder is enabled when the signal is zero (low).

Constructing Larger Decoders (1/4)

• Larger decoders can be constructed using smaller decoders.

Constructing Larger Decoders (2/4)

• This section includes circuit diagrams illustrating the construction of a 3x8 decoder from two 2x4 decoders, and an inverter.

Constructing Larger Decoders (3/4)

• 4x16 decoder is designed by combining two 3x8 decoders with appropriate enable signals and an inverter

Constructing Larger Decoders (4/4)

• How to construct a 4x16 decoder using five 2x4 decoders.
• A circuit to illustrate how decoders are connected to implement such a design.
• Output calculation for each output line based on selected input values

Negated Outputs (Active Low Outputs) Decoders

• Decoders can have active-low outputs.
• The output is low when the corresponding input code condition is met.

Standard MSI Decoder (1/2)

• Description of the 74138 3-to-8 decoder as an MSI component.
• Pin configuration and logic circuit diagrams.

Standard MSI Decoder (2/2)

• Function table explaining inputs and outputs for the 74138 decoder, and the general specification of the decoder.

Decoders: Implementing Functions Revisit (1/2)

• Example implementation of a Boolean function using 3x8, and OR/NAND gate
• Examples show how you can implement functions using decoders with different output characteristics.

Decoders: Implementing Functions Revisit (2/2)

• Example implementations of a specific function (f(Q,X,P)) using different decoder types (active high with OR gate, active low with NAND gate, active high NOR gate, active low AND gate).

Encoders (1/4)

• Encoders are the opposite of decoders: convert an active input to a coded output.
• It identifies a single active input and provides a corresponding code.

Encoders (2/4)

• Truth tables show how an encoder maps input lines to output codes.
• The function circuits are illustrated in the diagrams.

Encoders (3/4)

• A 8-to-3 Encoder is explained
• Truth tables map how encoder translates an input line to a specific code.

Encoders (4/4)

• A general 2^n to n encoder can also be implemented.
• Using example illustrating circuit for an 8-to-3 encoder, with a simple formula to identify the output.

Priority Encoders (1/2)

• Description of priority encoder to select the line with highest priority.

Priority Encoders (2/2)

• Detailed table for a 4-to-2 priority encoder.

Multiplexers (1/4)

• Multiplexers select data from multiple sources for a single output line.
• They function like a switch selector, choosing one input based on selection.

Multiplexers (2/4)

• Truth tables demonstrate the 4x1 multiplexer.

Multiplexers (3/4): Function Output Example

• Output of multiplexer as a sum of minterms relating selection and data lines expressed in terms of product terms.

Multiplexers (4/4): 2^n to 1 line multiplexer circuit

• A 2n-to-1 line multiplexer implementation with circuit design using a decoder and AND gates.

Multiplexer IC Package

• Some integrated circuits have multiple multiplexers on a single chip, with common enabling and selection.

Standard MSI Multiplexer (1/2)

• Overview of the 74151A 8 to 1 multiplexer, with package specification and function table.

Standard MSI Multiplexer (2/2): Detailed Diagram

• Logic diagram and general symbol for the 74151A 8-to-1 multiplexer.

Multiplexers: Implementing Functions (1/3)

• Implementing Boolean functions using multiplexers - method for implementing Boolean functions with a given multiplexer.

Multiplexers: Implementing Functions (2/3)

• Method for implementation, including output calculation.

Multiplexers: Implementing Functions (3/3)

• Example function implementation with a 74151A multiplexer.
• Truth table is given and illustrates the implementation with a logic circuit diagram.

Using Smaller Multiplexers (1/6)

• Implemetation of Boolean function using smaller multiplexers with steps

Using Smaller Multiplexers (2/6)

• Implementing Boolean functions in case of using a smaller size multiplexer with steps

Using Smaller Multiplexers (3/6)

• Procedure for implementing a Boolean function with smaller multiplexers

Using Smaller Multiplexers (4/6)

• Truth table to show relationship between input and output in use of smaller multiplexers

Using Smaller Multiplexers (5/6)

• Alternative implementation method in case of using multiplexers other than 8-to-1

Using Smaller Multiplexers (6/6)

• Example function implementation with a 74151A multiplexer.
• Truth table is given and illustrates the implementation using diagrams.