Binary Coded Decimal (BCD) is a numeral system that encodes each decimal digit (0-9) as a four-bit binary number. For example, the decimal number 1895 is represented in BCD as 0001 1000 1001 0101. The process of converting from binary to BCD involves first converting to decimal and then encoding each decimal digit as a four-bit binary equivalent.

1. What is BCD?

2. What is BCD
Binary coded decimal (BCD) is a system of writing
numerals that assigns a four-digit binary code to
each digit 0 through 9 in a decimal (base-10)
numeral.
The four-bit BCD code for any particular single base-
10 digit is its representation in binary notation, as
follows:
0 = 0000.
1 = 0001.
2 = 0010.

3. Numbers larger than 9, having two or more digits in
the decimal system, are expressed digit by digit in
binary coded decimal. For example, the BCD
rendition of the base-10 number 1895 is 0001 1000
1001 0101. The binary equivalents of 1, 8, 9, and 5,
always in a four- digit format, go from left to
right. The BCD representation of a number is not
the same, in general, as its simple binary
representation. In binary form, for example, the
decimal quantity 1895 appears as 11101100111.

4. Binary to Decimal to BCD Conversion
Example
Binary Coded Decimal which is also called as BCD is another
process for converting decimal numbers into their binary
equivalents.
BCD Conversion Steps:
• Step 1 : Convert the binary number to decimal.
• Step 2 : Convert decimal number to BCD.
• Example: Convert (11101)2 to BCD
Step 1 : Convert to Decimal from Binary Number
• (11101)2 = (1×24)+ (1×23)+(1×22)+(0×21)+(1×20)=(1×16)+
(1×8) +(1×4)+ (0×2)+(1×1)= 16 + 8 + 4 + 0 + 1 = (29)10

5. Step 2 : Convert to BCD from Decimal Number =
(29)10 Calculating BCD Equivalent. Convert each
digit into groups of four binary digits equivalent.
Decimal Number Conversion
(29)10 = (0010)2 (1001)2
(29)10 = (00101001) BCD
Therefore 0010 1001 is the BCD code for
decimal 29.

6. BCD numbering system
BCD numbering system is very easy to understand, while
creating BCD each decimal number is separated into
equivalent four bits for each decimal digit within the
number. In the final result each decimal digit is replaced
by its weighted binary value performing a direct
translation of the number. Every 4-bit group represents
each displayed decimal digit from 0000 for a zero
to 1001 for a nine.
For example:
35710 (Three Hundred and Fifty Seven) in decimal would
be presented in Binary Coded Decimal as:
35710 = 0011 0101 0111 (resulted BCD)