Question

Define binary-coded decimal (BCD) and its representation.

Answer 1

Binary-coded decimal (BCD) is a binary-encoded numerical representation scheme used to store and manipulate decimal numbers in a digital format. Unlike the standard binary representation where each digit of a number is represented using a fixed number of bits (usually 4 or 8 bits), BCD uses a group of 4 bits to represent each individual decimal digit. In BCD, each decimal digit is encoded separately into its binary equivalent.

In BCD representation, each decimal digit (0 to 9) is represented using a 4-bit binary code. The four bits of a BCD digit represent the values 2^3 (8), 2^2 (4), 2^1 (2), and 2^0 (1), with each bit's position corresponding to a power of 2. Here's an example to illustrate BCD encoding:

Decimal Digit: 5
BCD Representation: 0101

Decimal Digit: 9
BCD Representation: 1001

Decimal Digit: 0
BCD Representation: 0000

Decimal Digit: 3
BCD Representation: 0011

BCD allows each decimal digit to be stored as a separate binary value, making it useful for applications where decimal arithmetic is more intuitive and required, such as financial calculations or displaying numbers on digital displays. However, BCD representation is less space-efficient compared to pure binary representation, as it uses more bits to represent the same range of values.