Binary Coded Decimal Numbers BCD

Another number system that is encountered occasionally is Binary Coded Decimal. In this system, numbers are represented in a decimal form, however each decimal digit is encoded using a four bit binary number.

For example: The decimal number 136 would be represented in BCD as follows:

136 = 0001 0011 0110

1        3         6

Conversion of numbers between decimal and BCD is quite simple. To convert from decimal to BCD, simply write down the four bit binary pattern for each decimal digit. To convert from BCD to decimal, divide the number into groups of 4 bits and write down the corresponding decimal digit for each 4 bit group.

There are a couple of variations on the BCD representation, namely packed and unpacked. An unpacked BCD number has only a single decimal digit stored in each data byte. In this case, the decimal digit will be in the low four bits and the upper 4 bits of the byte will be 0. In the packed BCD representation, two decimal digits are placed in each byte. Generally, the high order bits of the data byte contain the more significant decimal digit.

An example: The following is a 16 bit number encoded in packed BCD format:

01010110 10010011

This is converted to a decimal number as follows:

0101 0110 1001 0011

5      6        9        3

The value is 5693 decimal

Another example: The same number in unpacked BCD (requires 32 bits)

00000101 00000110 00001001 00000011

5                 6                 9               3

The use of BCD to represent numbers isn’t as common as binary in most computer systems, as it is not as space efficient. In packed BCD, only 10 of the 16 possible bit patterns in each 4 bit unit are used. 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.



Abbreviation of Extended Binary-Coded Decimal Interchange Code. Pronounced eb-sih-dik, EBCDIC is an IBM code for representing characters as numbers. Although it is widely used on large IBM computers, most other computers, including PCs and Macintoshes, use ASCII codes.

ASCII Character Encoding

The name ASCII is an acronym for: American Standard Code for Information Interchange. It is a character encoding standard developed several decades ago to provide a standard way for digital machines to encode characters. The ASCII code provides a mechanism for encoding alphabetic characters, numeric digits, and punctuation marks for use in representing text and numbers written using the Roman alphabet.

As originally designed, it was a seven bit code. The seven bits allow the representation of 128 unique characters. All of the alphabet, numeric digits and standard English punctuation marks are encoded. The ASCII standard was later extended to an eight bit code (which allows 256 unique code patterns) and various additional symbols were added, including characters with diacritical marks (such as accents) used in European languages, which don’t appear in English.

There are also numerous non-standard extensions to ASCII giving different encoding for the upper 128 character codes than the standard. For example, The character set encoded into the display card for the original IBM PC had a non-standard encoding for the upper character set. This is a non-standard extension that is in very wide spread use, and could be considered a standard in itself.

Some important things to note about ASCII code:

1) The numeric digits, 0-9, are encoded in sequence starting at 30h

2) The upper case alphabetic characters are sequential beginning at 41h

3) The lower case alphabetic characters are sequential beginning at 61hEE-314 Number Systems 7

4) The first 32 characters (codes 0-1Fh) and 7Fh are control characters. They do not have a standard symbol (glyph) associated with them. They are used for carriage control, and protocol purposes. They include 0Dh (CR or carriage return), 0Ah (LF or line feed), 0Ch (FF or form feed), 08h (BS or backspace).

5) Most keyboards generate the control characters by holding down a control key (CTRL) and simultaneously pressing an alphabetic character key. The control code will have the same value as the lower five bits of the alphabetic key pressed. So, for example, the control character 0Dh is carriage return. It can be generated by pressing CTRL-M. To get the full 32 control characters a few at the upper end of the range are generated by pressing CTRL and a punctuation key in combination. For example, the ESC (escape) character is generated by pressing CTRL-[ (left square bracket).


 Conversions Between Upper and Lower Case ASCII Letters.

Notice on the ASCII code chart that the uppercase letters start at 41h and that the lower case letters begin at 61h. In each case, the rest of the letters are consecutive and in alphabetic order. The difference between 41h and 61h is 20h. Therefore the conversion between upper and lower case involves either adding or subtracting 20h to the character code.

To convert a lower case letter to upper case, subtract 20h, and conversely to convert upper case to lower case, add 20h. It is important to note that you need to first ensure that you do in fact have an alphabetic character before performing the addition or subtraction. Ordinarily, a check should be made that the character is in the range 41h–5Ah for upper case or 61h-7Ah for lower case.


Conversion Between ASCII and BCD.

Notice also on the ASCII code chart that the numeric characters are in the range 30h-39h. Conversion between an ASCII encoded digit and an unpacked BCD digit can be accomplished by adding or subtracting 30h. Subtract 30h from an ASCII digit to get BCD, or add 30h to a BCD digit to get ASCII. Again, as with upper and lower case conversion for alphabetic characters, it is necessary to ensure that the character is in fact a numeric digit before performing the subtraction. The digit characters are in the range 30h-39h

ASCII Character Set






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