BCD Digit Bit Requirement Explained

The question asks about the number of bits required to store a single Binary-Coded Decimal (BCD) digit. Let's break down what BCD is and how it works.

Understanding Binary-Coded Decimal (BCD)

Binary-Coded Decimal, or BCD, is a way to represent decimal numbers (0 through 9) using binary codes. Unlike standard binary representation, where a number like 12 would be represented as $1100_2$, BCD represents each decimal digit individually using a fixed number of bits.

In BCD, each decimal digit from 0 to 9 is encoded using its own 4-bit binary equivalent. This ensures that the binary pattern for each digit is easily recognizable.

BCD Representation Table

Here's how the decimal digits 0 through 9 are represented in BCD:

Why 4 Bits Are Necessary

To represent 10 different decimal digits (0 to 9), we need at least 10 distinct binary patterns. Let's see how many patterns we can make with different numbers of bits:

• 1 bit: Can represent $2^1 = 2$ patterns ($0_2$, $1_2$). Not enough.
• 2 bits: Can represent $2^2 = 4$ patterns ($00_2$, $01_2$, $10_2$, $11_2$). Not enough.
• 3 bits: Can represent $2^3 = 8$ patterns ($000_2$ to $111_2$). Still not enough.
• 4 bits: Can represent $2^4 = 16$ patterns ($0000_2$ to $1111_2$). This is sufficient to represent the 10 required decimal digits (0-9).

Since BCD uses a 4-bit pattern for each decimal digit, and the highest value needed is 9 ($1001_2$), 4 bits are the standard and necessary amount.

Conclusion on BCD Bits

Therefore, the number of bits used to store a single BCD digit is 4.