The correct answer is A. 1 and 2.
Shift registers and modulo-2 adders are the two basic building blocks of encoders and decoders used for the implementation of cyclic codes.
A shift register is a sequential logic circuit that stores a sequence of bits. The bits are stored in a series of registers, which are connected in a loop. The bits are shifted in and out of the registers one at a time, according to a clock signal.
A modulo-2 adder is a logic circuit that adds two binary numbers modulo 2. This means that the adder only produces a carry bit if the sum of the two numbers is greater than 1.
Encoders and decoders are used to convert between binary numbers and code words. An encoder takes a binary number as input and produces a code word as output. A decoder takes a code word as input and produces the corresponding binary number as output.
Cyclic codes are a type of error-correcting code. They are used to detect and correct errors in data transmission. Cyclic codes are implemented using shift registers and modulo-2 adders.
The following is a brief explanation of each option:
- Option 1: Shift registers are present in encoders and decoders used for the implementation of cyclic codes. Shift registers are used to store the code words.
- Option 2: Modulo-2 adders are present in encoders and decoders used for the implementation of cyclic codes. Modulo-2 adders are used to add the code words.
- Option 3: Counters are not present in encoders and decoders used for the implementation of cyclic codes. Counters are used to generate the clock signal.
- Option 4: Multiplexers are not present in encoders and decoders used for the implementation of cyclic codes. Multiplexers are used to select between two or more signals.