To convert BCD to Decimal, input BCD in the box below, and then click on the big blue button that says “CONVERT TO Decimal” and text is generated, copy it or you can download output file.
In BCD, numbers are represented in a decimal form, however each decimal digit is encoded using a four bit binary number.
For example: The decimal number 160 would be represented in BCD as follows:
160 = 0001 0110 0000
1 6 0
In decimal number system there only ten (10) digits from 0 to 9. Every number (value) in this decimal system represents with 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base of this number system is 10, because it has only 10 digits.
For Example: 8062 in decimal (base 10)
7562_{10} = (7 x 10^{3}) + (5 x 10^{2}) + (6 x 10^{1}) + (2 x 10^{0})
Converting a BCD to Decimal is quite simple.
Step 1: If you want to convert a number from BCD to simply divide the binary number into groups of four digits, starting with the least significant digit.
Step 2: Now raise it to a power of 0 and increase that power by 1 each time according to the hexadecimal number equivalent.
Example 1: Convert the following binary numbers: 101_{2}, 1110_{2}, 1001001_{2} and 10100111001.101_{2} into their decimal equivalents.
101_{2} = 0101_{BCD} = 5_{10}
1110_{2} = this will produce an error as it is decimal 10_{10} and not a valid BCD number
1001001_{2} = 0100 1001_{BCD} = 49_{10}
10100111001.101_{2} = 0101 0011 1001.1010_{BCD} = 539.625_{10}
DECIMAL | BCD |
---|---|
0 | 0000 |
1 | 0001 |
2 | 0010 |
3 | 0011 |
4 | 0100 |
5 | 0101 |
6 | 0110 |
7 | 0111 |
8 | 1000 |
9 | 1001 |
The use of BCD isn’t as common as binary in most computer systems because it is not as space-efficient. If we talk about packed BCD, only 10 of the 16 possible bit patterns in each 4 bit unit are used. While in unpacked BCD, only 10 of the 256 possible bit patterns in each byte are used. A 16 bit quantity can represent the range 0-65535 in binary, 0-9999 in packed BCD and only 0-99 in unpacked BCD.