BCD Conversion Explained

Understanding how to convert numbers from one base to another is a fundamental concept in digital electronics and computer science. The question asks for the BCD equivalent of (345)₁₀. BCD stands for Binary Coded Decimal. It's a way to represent decimal numbers where each decimal digit is encoded separately into its 4-bit binary equivalent. This is different from a pure binary conversion where the entire number is converted to binary.

Decimal to BCD Conversion Steps

To find the BCD equivalent of (345)₁₀, we need to take each digit of the decimal number (3, 4, and 5) and convert it into its 4-bit binary representation.

1. First Digit (3): The decimal digit 3 in 4-bit binary is 0011.
2. Second Digit (4): The decimal digit 4 in 4-bit binary is 0100.
3. Third Digit (5): The decimal digit 5 in 4-bit binary is 0101.

Once each decimal digit is converted, we simply concatenate these 4-bit binary codes in the same order as the decimal digits.

Therefore, the BCD equivalent of (345)₁₀ is the combination of these binary codes:

3 → 0011

4 → 0100

5 → 0101

Concatenating them gives: 0011 0100 0101

BCD Encoding Table

Here is a useful table showing the 4-bit BCD codes for decimal digits 0 through 9:

Using this table, we can easily verify the conversion for (345)₁₀:

• The digit 3 maps to 0011.
• The digit 4 maps to 0100.
• The digit 5 maps to 0101.

Combining these directly yields 0011 0100 0101.

Comparing with Options

Let's evaluate the given options based on our understanding of BCD equivalent:

• 0011 1001 1010: This option is incorrect. While the first part (0011 for 3) is correct, the subsequent parts (1001 for 9, 1010 is not a valid BCD code for a single digit) do not correspond to 4 and 5.
• 1001 1001 1111: This option is incorrect. None of the parts correspond to the digits 3, 4, or 5 in BCD.
• 0011 0100 0101: This option correctly represents 3 (0011), 4 (0100), and 5 (0101) in BCD. This matches our calculated BCD equivalent.
• 0101 1100 1001: This option is incorrect. It starts with 0101 (for 5), then 1100 (not a valid BCD digit), and 1001 (for 9). It does not match the digits of 345.

Therefore, the correct BCD equivalent of (345)₁₀ is 0011 0100 0101.