Understanding 4-Bit BCD Code

BCD stands for Binary-Coded Decimal. It's a way to represent decimal numbers (0 through 9) using binary digits (bits). In BCD, each decimal digit is represented by its equivalent 4-bit binary code.

A 4-bit binary code can represent numbers from $0000_2$ to $1111_2$. In standard binary, this range corresponds to decimal values from $0_{10}$ to $15_{10}$.

However, BCD is specifically designed to represent decimal digits. There are only ten decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Each of these decimal digits is assigned a unique 4-bit binary code in the BCD system:

• Decimal 0 is $0000_2$
• Decimal 1 is $0001_2$
• Decimal 2 is $0010_2$
• Decimal 3 is $0011_2$
• Decimal 4 is $0100_2$
• Decimal 5 is $0101_2$
• Decimal 6 is $0110_2$
• Decimal 7 is $0111_2$
• Decimal 8 is $1000_2$
• Decimal 9 is $1001_2$

The 4-bit binary codes from $1010_2$ to $1111_2$ (which represent decimal 10 to 15 in standard binary) are considered invalid in the BCD system for a single digit representation.

Therefore, when representing a single decimal digit using 4-bit BCD, the largest possible decimal digit is 9, which is represented by the binary code $1001_2$.

For numbers larger than 9, multiple 4-bit BCD groups are used, one for each decimal digit. For example, the decimal number 24 would be represented as two 4-bit BCD codes: 0010 (for 2) and 0100 (for 4), resulting in 0010 0100 BCD.

The question asks for the maximum number represented by 4 bit BCD code, implying the maximum value representable by a single 4-bit BCD group, which is used for one decimal digit. This maximum decimal digit is 9.