What is bcd number

By clicking sign up, you agree to receive emails from Techopedia and agree to our Terms of Use and Privacy Policy. A binary-coded decimal BCD is a type of binary representation for decimal values where each digit is represented by a fixed number of binary bits, usually between four and eight. The norm is four bits, which effectively represent decimal values 0 to 9. This writing format system is used because there is no limit to the size of a number.

Four bits can simply be added as another decimal digit, versus real binary representation, which is limited to the usual powers of two, such as 16, 32 or 64 bits. By: Justin Stoltzfus Contributor, Reviewer. By: Satish Balakrishnan. Dictionary Dictionary Term of the Day. Gorilla Glass. Binary coded decimal has specifically important applications using digital displays. This system is a Base-2 numbering system which follows the same set of rules used with decimal or base number system.

Base uses powers of ten, for example 1, 10, , and so on, where binary numbers use powers of two, effectively doubling the value of each sequential bit, for example 1, 2, 4, 8, 16, 32 and so on. This conversion between binary and decimal values is called Binary-coded decimal and allows for easy conversion between decimal and binary numbers.

Binary-coded decimal or BCD is a code using a series of binary digits or bits that when decoded represents a decimal digit. So, each decimal digit 0 through 9 is represented by a series of four binary bits where the numerical value when decoded is equivalent to a decimal digit.

As you can see in the illustration below, the decimal weight of each decimal digit to the left increases by a factor of The first digit has a weight of 1 or 2 0 , the second digit has a weight of 2 or 2 1 , the third digit has a weight of 4 or 2 2 , and the fourth digit has a weight of 8 or 2 3.

Now with the basic understanding of the binary-weighted system, the relationship between decimal numbers and weighted binary coded decimal digits for decimal values of 0 through 15 are provided as a truth table for BCD. Keep in mind, Binary-coded decimal is not the same as binary to decimal conversion.

For example, if I would represent the decimal number 72 in both forms, the bit formation would be like this:. When we use a table to explain and expand out the weighted values, using 16 bits, we can convert the following decimal numbers: , and into their binary equivalents. By adding together all the decimal number values from right to left from each of the bit positions that are represented by a 1 gives us the decimal equivalent.

Analog Circuits amplify varying voltage levels that can alternate between a positive and negative value over a period of time and Digital Circuits produce distinct positive or negative voltage levels representing either a logic level 1 or a logic level 0 state. Voltages used in digital circuits could be any value, however in digital and computer systems they are below 10 volts.

In digital circuits voltages are called logic levels and typically one voltage level will represent a HIGH state, and the lower voltage level will represent a LOW state. A binary clock might use LEDs to express binary values. With this clock each column of LEDs displays a binary-coded decimal numeral. Back in the days, before touchscreens, seven segment displays , and thumbwheel switches were used for a numerical interface between PLCs and humans. Even before the PLC, these BCD type devices were the only graphical way to interface with system circuits numerically.

Some PLCs for example, Siemens S7 standard timer and counter data types use Binary Coded Decimal in their data structures because these structures go back to when engineers had to deal with things like these thumbwheels and 7 segment displays. These timers use three BCD digits or 12 bits and two extra bits for the time base. If you would like to get additional training on a similar subject please let us know in the comment section.

When the binary number is 0, then the number is off, when the binary number is 1, then the number is on. The following is an example of binary digits and how they represent decimal digits:.

For every decimal number added, you add 4-bits or one nibble. Binary numbers are limited to the largest number that can be represented by 8, 16, 32 and 64 bits. It is easier to convert decimal numbers to and from BCD than Binary. However, hardware can be built to operate directly with BCD.