Q.Convert $823_{10}$ to BCD

The Binary Coded Decimal (BCD) and Excess-3 codes are the two most common ways of coding individual decimal digits for digital arithmetic.

In the standard 8-4-2-1 BCD code, each decimal digit from 0 to 9 is written as its ordinary 4-bit binary value. To code a multi-digit number, each decimal digit is converted separately; for example $823_{10} = 1000\;0010\;0011_{BCD}$. Because only ten of the sixteen possible 4-bit patterns are used, the combinations 1010 to 1111 are invalid in BCD. Converting back is just as direct — a BCD group is split into 4-bit fields and each field is read as one decimal digit.

The Excess-3 code is formed by adding 3 (binary 0011) to the 8-4-2-1 BCD value of each digit. For example, decimal 18 has BCD $0001\;1000$ and Excess-3 $0100\;1011$. Excess-3 is a non-weighted code, so its bits carry no positional weight, but it is self-complementing: the 9's complement of a digit is obtained by simply inverting each bit. This property makes Excess-3 attractive for arithmetic circuits that need decimal subtraction.

Typical operations you must be able to perform include decimal-to-BCD conversion, BCD-to-decimal and BCD-to-binary conversion, finding the 9's complement of a BCD number, and coding a digit in Excess-3. These conversions appear repeatedly as solved examples and short-answer questions.