The BCD to Decimal Calculator is a tool designed to simplify the conversion of Binary-Coded Decimal (BCD) numbers into standard decimal format. BCD is a class of binary encodings where each decimal digit is represented by a fixed number of binary digits, usually four or eight. This calculator helps you quickly and accurately convert these BCD numbers into their decimal equivalents.
Using this calculator, you can save time and reduce the risk of errors that might occur during manual conversion. It is especially useful for students, educators, and professionals who frequently work with digital systems and need to perform such conversions.
Formula of BCD to Decimal Calculator
Group the BCD Digits
To convert a BCD number to a decimal number, start by grouping the BCD digits into sets of four bits, beginning from the least significant bit (rightmost). If the total number of bits is not a multiple of four, pad the leftmost side with zeros to make complete groups.
Convert Each Group to Decimal
Next, treat each 4-bit group as a separate binary number and convert it to its decimal equivalent. You can use a simple binary to decimal conversion table for this process or perform the conversion manually.
Combine the Decimal Values
After converting each group to decimal, write down the decimal value for each group. The rightmost decimal value corresponds to the least significant digit in the final decimal number. By reading these decimal digits from right to left, you form the converted decimal number.
Binary to Decimal Conversion Table
| BCD (4 bits) | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
Example of BCD to Decimal Calculator
Let’s go through an example to understand the conversion process better. Suppose we have a BCD number 1001 0011.
- Group the BCD Digits: The BCD number
1001 0011is already grouped into two sets of four bits. - Convert Each Group to Decimal:
- The first group
1001converts to9in decimal. - The second group
0011converts to3in decimal.
- The first group
- Combine the Decimal Values: Reading from right to left, the decimal number is
93.
Most Common FAQs
BCD stands for Binary-Coded Decimal. It is a method of encoding decimal numbers in which each digit is represented by a fixed number of binary digits, typically four or eight.
In standard binary representation, the entire number is convert into binary form. In BCD, each individual decimal digit is represent by its own binary sequence. This makes BCD easier to read and convert manually.
BCD is often use in digital systems where readability and ease of conversion between binary and decimal are important. It is particularly useful in applications like digital clocks and calculators where human-readable digits are need.