BCD Code Bits Per Number Explained

Binary Coded Decimal (BCD) is a method used in digital electronics and computer science to represent decimal numbers. In BCD, each decimal digit from 0 to 9 is encoded using a specific number of binary bits.

Understanding BCD Representation

The core idea of BCD is to use a fixed binary pattern for each decimal digit. Since there are 10 decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), we need enough bits to represent all of them uniquely. Let's see how many bits are required:

• With 1 bit, we can represent $2^1 = 2$ values (0, 1). Not enough for 10 digits.
• With 2 bits, we can represent $2^2 = 4$ values (00, 01, 10, 11). Still not enough.
• With 3 bits, we can represent $2^3 = 8$ values (000 to 111). Still not enough.
• With 4 bits, we can represent $2^4 = 16$ values (0000 to 1111). This is sufficient to represent the 10 decimal digits (0 through 9).

Standard BCD Format

The standard BCD code assigns a unique 4-bit binary number to each decimal digit:

• Decimal 0 is represented as 0000
• Decimal 1 is represented as 0001
• Decimal 2 is represented as 0010
• ...and so on, up to...
• Decimal 9 is represented as 1001

Notice that the binary patterns from 1010 (10 in decimal) to 1111 (15 in decimal) are unused in the standard 8-4-2-1 BCD code because they are not needed to represent single decimal digits.

Therefore, BCD code consistently uses 4 bits for each decimal number (digit).