Decimal-to-BCD Encoder

The Decimal-to-BCD (Binary-Coded Decimal) encoder is a combinational logic circuit that converts a decimal number to its BCD equivalent. BCD is a binary representation of a decimal number where each decimal digit is represented by a 4-bit binary code.

The BCD code uses four binary bits to represent each decimal digit from 0 to 9. In BCD, the binary codes for 0 to 9 are 0000 to 1001, respectively. For example, the decimal number 7 is represented in BCD as 0111.

To design a Decimal-to-BCD encoder, we need to analyze the input and output requirements.

Input: The input to the Decimal-to-BCD encoder is a 4-bit binary number representing a decimal digit. Since we are converting decimal numbers from 0 to 9, the input can have 10 possible combinations from 0000 to 1001.

Output: The output of the Decimal-to-BCD encoder is a 4-bit BCD code for the input decimal digit. Since each decimal digit is represented by a 4-bit BCD code, the output will also have 4 bits.

Logic Design: To convert a 4-bit binary number to its BCD equivalent, we need to implement a logic circuit that maps each possible input combination to its corresponding BCD output.

- We can use a truth table to determine the required logic for the Decimal-to-BCD encoder.
- The truth table will have 10 rows (for 10 input combinations from 0000 to 1001) and 4 columns (for the 4 output bits of the BCD code).
- By analyzing the truth table, we can determine the logic expressions for each output bit.

Number of OR Gates:

- The Decimal-to-BCD encoder requires 4 output bits, and each output bit can be implemented using an OR gate.
- As the correct answer is option 'D', which states that 4 OR gates are required, it aligns with the requirement of having 4 output bits in the Decimal-to-BCD encoder.

Therefore, the correct answer is option 'D' - 4.