Decoder IC
A decoder IC is a digital integrated circuit that converts coded inputs into corresponding outputs. It is commonly used in digital systems to decode binary information and control multiple output devices based on the input signals. Among the given options, the correct answer is option 'B', which is the 8870 decoder IC.

Explanation

Let's discuss each option one by one to understand why option 'B' is the correct answer.

a) 7890
The number '7890' does not correspond to any known decoder IC. It is not a valid option.

b) 8870
The 8870 is indeed a decoder IC. It is a DTMF (Dual Tone Multi-Frequency) decoder IC that is used to decode the DTMF signals generated by a telephone keypad. The DTMF signals consist of two frequencies, one from a low group and the other from a high group, which are used to represent different digits and symbols. The 8870 decoder IC can detect and decode these frequencies to provide a corresponding binary output.

c) 4047
The 4047 is not a decoder IC. It is a multivibrator IC that is commonly used for generating square waves and other timing signals in electronic circuits. It does not perform the function of decoding inputs.

d) 4041
The 4041 is not a decoder IC either. It is a quad D-type flip-flop IC that is used for storing and manipulating binary data. It does not have the capability to decode inputs.

Conclusion
Among the given options, the correct answer for a decoder IC is option 'B', which is the 8870 decoder IC. The 8870 is specifically designed to decode DTMF signals, making it suitable for applications such as telecommunication systems and remote control systems.