15.3 Encoders and decoders

Encoders and decoders are essential components in digital systems, converting data between different formats. Encoders transform higher-radix inputs to lower-radix outputs, while decoders do the opposite. These devices are crucial for tasks like keyboard input processing and memory address decoding.

Priority encoders handle multiple active inputs, outputting the highest-priority one. BCD decoders convert binary to decimal for displays. 7-segment display decoders drive LED displays, enabling the visual representation of numbers in various electronic devices. These components form the backbone of many digital interfaces we use daily.

Encoder and Decoder Fundamentals

Encoders

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• Encoders convert data from one format to another, typically from a higher-radix input to a lower-radix output (decimal to binary)
• Encoders have $2^n$ input lines and $n$ output lines
• Input lines are typically labeled with the corresponding binary value they represent (0, 1, 2, 3, etc.)
• Output lines are labeled with the corresponding bit position they represent (A, B, C, etc.)
• When an input line is activated, the corresponding binary code appears on the output lines
• Encoders are used in applications such as keyboards, where pressing a key generates a unique binary code

Decoders

• Decoders perform the opposite function of encoders, converting data from a lower-radix input to a higher-radix output (binary to decimal)
• Decoders have $n$ input lines and $2^n$ output lines
• Input lines are labeled with the corresponding bit position they represent (A, B, C, etc.)
• Output lines are typically labeled with the corresponding decimal value they represent (0, 1, 2, 3, etc.)
• When a binary code is applied to the input lines, the corresponding output line is activated
• Decoders are used in applications such as memory address decoding and data demultiplexing

Binary Coding and Enable Inputs

• Binary coding is used to represent data in encoders and decoders
• Each input or output line corresponds to a specific binary value or bit position
• Enable inputs are used to control the operation of encoders and decoders
• When the enable input is active, the device performs its normal encoding or decoding function
• When the enable input is inactive, the device is disabled, and its outputs are typically forced to a known state (all 0s or all 1s)
• Enable inputs allow multiple encoders or decoders to be connected to a common bus without causing conflicts

Encoder Types and Applications

Priority Encoders

• Priority encoders are a type of encoder that assigns a priority to each input line
• When multiple input lines are active simultaneously, the priority encoder outputs the binary code corresponding to the highest-priority active input
• Priority encoders have an additional output called the "valid" or "any" output, which indicates whether any input lines are active
• Priority encoders are used in applications such as interrupt handling in microprocessors, where multiple interrupt sources may be active simultaneously, and the highest-priority interrupt must be serviced first
• Example: In a 4-input priority encoder, if inputs 2 and 3 are active, the output will be the binary code for input 3 (11), since it has a higher priority than input 2

Decoder Types and Applications

BCD Decoders

• BCD (Binary-Coded Decimal) decoders convert a 4-bit binary input representing a decimal digit (0-9) into a 10-line decimal output
• BCD decoders are commonly used in digital displays and calculators to convert binary data into a format that can be easily displayed
• Example: A BCD decoder with inputs A=1, B=0, C=0, D=1 will activate output line 9, as the binary input 1001 represents the decimal digit 9

7-Segment Display Decoders

• 7-segment display decoders convert a 4-bit binary input into the signals needed to drive a 7-segment LED display
• 7-segment displays consist of seven LED segments (a, b, c, d, e, f, g) arranged in a figure-8 pattern, plus an optional decimal point (dp)
• Each segment is controlled by a separate output from the decoder
• By activating the appropriate segments, any decimal digit (0-9) can be displayed
• 7-segment display decoders are used in a wide range of applications, including digital clocks, calculators, and instrumentation
• Example: To display the digit "5" on a 7-segment display, the decoder would activate segments a, f, g, c, and d, while leaving segments b and e inactive