2.6.1 Binary-Coded Decimal

Binary-coded decimal (BCD) is a numeric coding system used primarily in IBM mainframe and midrange systems. As its name implies, BCD encodes each digit of a decimal number to a 4-bit binary form. When stored in an 8-bit byte, the upper nibble is called the zone and the lower part is called the digit. (This convention comes to us from the days of punched cards where each column of the card could have a "zone punch" in one of the top 2 rows and a "digit punch" in one of the 10 bottom rows.) The high-order nibble in a BCD byte is used to hold the sign, which can have one of three values: An unsigned number is indicated with 1111; a positive number is indicated with 1100; and a negative number is indicated with 1101. Coding for BCD numbers is shown in Figure 2.5.

Figure 2.5: Binary-Coded Decimal

As you can see by the figure, six possible binary values are not used, 1010 through 1111. Although it may appear that nearly 40% of our values are going to waste, we are gaining a considerable advantage in accuracy. For example, the number 0.3 is a repeating decimal when stored in binary. Truncated to an 8-bit fraction, it converts back to 0.296875, giving us an error of approximately 1.05%. In BCD, the number is stored directly as 1111 0011 (we are assuming the decimal point is implied by the data format), giving no error at all.

The digits of BCD numbers occupy only one nibble, so we can save on space and make computations simpler when adjacent digits are placed into adjacent nibbles, leaving one nibble for the sign. This process is known as packing and numbers thus stored are called packed decimal numbers.

Example 2.26:

Represent –1265 in 3 bytes using packed BCD.

The zoned-decimal coding for 1265 is:

1111 0001 1111 0010 1111 0110 1111 0101

After packing, this string becomes:

0001 0010 0110 0101

Adding the sign after the low-order digit and padding the high-order digit with ones in 3 bytes we have:

2.6.2 EBCDIC

Before the development of the IBM System/360, IBM had used a 6-bit variation of BCD for representing characters and numbers. This code was severely limited in how it could represent and manipulate data; in fact, lowercase letters were not part of its repertoire. The designers of the System/360 needed more information processing capability as well as a uniform manner in which to store both numbers and data. In order to maintain compatibility with earlier computers and peripheral equipment, the IBM engineers decided that it would be best to simply expand BCD from 6 bits to 8 bits. Accordingly, this new code was called Extended Binary Coded Decimal Interchange Code (EBCDIC). IBM continues to use EBCDIC in IBM mainframe and midrange computer systems. The EBCDIC code is shown in Figure 2.6 in zone-digit form. Characters are represented by appending digit bits to zone bits. For example, the character a is 1000 0001 and the digit 3 is 1111 0011 in EBCDIC. Note the only difference between upperand lowercase characters is in bit position 2, making a translation from upperto lowercase (or vice versa) a simple matter of flipping one bit. Zone bits also make it easier for a programmer to test the validity of input data.

Figure 2.6: The EBCDIC Code (Values Given in Binary Zone-Digit Format)

2.6.3 ASCII

While IBM was busy building its iconoclastic System/360, other equipment makers were trying to devise better ways for transmitting data between systems. The American Standard Code for Information Interchange (ASCII) is one outcome of these efforts. ASCII is a direct descendant of the coding schemes used for decades by teletype (telex) devices. These devices used a 5-bit (Murray) code that was derived from the Baudot code, which was invented in the 1880s. By the early 1960s, the limitations of the 5-bit codes were becoming apparent. The International Organization for Standardization (ISO) devised a 7-bit coding scheme that it called International Alphabet Number 5. In 1967, a derivative of this alphabet became the official standard that we now call ASCII.

As you can see in Figure 2.7, ASCII defines codes for 32 control characters, 10 digits, 52 letters (upperand lowercase), 32 special characters (such as $ and #), and the space character. The high-order (eighth) bit was intended to be used for parity.

Figure 2.7: The ASCII Code (Values Given in Decimal)

Parity is the most basic of all error detection schemes. It is easy to implement in simple devices like teletypes. A parity bit is turned "on" or "off" depending on whether the sum of the other bits in the byte is even or odd. For example, if we decide to use even parity and we are sending an ASCII A, the lower 7 bits are 1000001. Because the sum of the bits is even, the parity bit would be set to off and we would transmit 0100 0001. Similarly, if we transmit an ASCII C, 100 0011, the parity bit would be set to on before we sent the 8-bit byte, 1100 0011. Parity can be used to detect only single-bit errors. We will discuss more sophisticated error detection methods in Section 2.8.

To allow compatibility with telecommunications equipment, computer manufacturers gravitated toward the ASCII code. As computer hardware became more reliable, however, the need for a parity bit began to fade. In the early 1980s, microcomputer and microcomputer-peripheral makers began to use the parity bit to provide an "extended" character set for values between 128₁₀ and 255_10.

Depending on the manufacturer, the higher-valued characters could be anything from mathematical symbols to characters that form the sides of boxes to foreign-language characters such as ñ. Unfortunately, no amount of clever tricks can make ASCII a truly international interchange code.

2.6.4 Unicode

Both EBCDIC and ASCII were built around the Latin alphabet. As such, they are restricted in their abilities to provide data representation for the non-Latin alphabets used by the majority of the world's population. As all countries began using computers, each was devising codes that would most effectively represent their native languages. None of these were necessarily compatible with any others, placing yet another barrier in the way of the emerging global economy.

In 1991, before things got too far out of hand, a consortium of industry and public leaders was formed to establish a new international information exchange code called Unicode. This group is appropriately called the Unicode Consortium.

Unicode is a 16-bit alphabet that is downward compatible with ASCII and the Latin-1 character set. It is conformant with the ISO/IEC 10646-1 international alphabet. Because the base coding of Unicode is 16 bits, it has the capacity to encode the majority of characters used in every language of the world. If this weren't enough, Unicode also defines an extension mechanism that will allow for the coding of an additional million characters. This is sufficient to provide codes for every written language in the history of civilization.

The Unicode codespace consists of five parts, as shown in Figure 2.8. A full Unicode-compliant system will also allow formation of composite characters from the individual codes, such as the combination of ´ and A to form Á. The algorithms used for these composite characters, as well as the Unicode extensions, can be found in the references at the end of this chapter.

Figure 2.8: Unicode Codespace

Although Unicode has yet to become the exclusive alphabet of American computers, most manufacturers are including at least some limited support for it in their systems. Unicode is currently the default character set of the Java programming language. Ultimately, the acceptance of Unicode by all manufacturers will depend on how aggressively they wish to position themselves as international players and how inexpensively disk drives can be produced to support an alphabet with double the storage requirements of ASCII or EBCDIC.