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Chapter 3

Data Types and Data Storage

In this chapter we review the various encodings and formats used for representing character and numeric data in digital systems. Tha character formats are used for encoding the letters, symbols, and control codes of the various alphabets. The numeric formats allow representing binary numbers as signed and unsigned integers in several forms, binary floating-point numbers, and decimal floating-point numbers, usually called binary-coded decimals or BCD.

3.0 Electronic-Digital Machines

The mechanization of arithmetic is often traced back to the abacus, slide rule, mechanical calculators, and punch card machines. The work of John von Neumann at Princeton’s Institute for Advanced Study and Research marks the first highlight in the design and construction of a digital-electronic calculating machine. In von Neumann’s design, data and instructions are stored in a common memory area. An alternative approach, known as Harvard architecture, was discarded at first but has recently been re-validated and is in use in several microcontroller families.

The calculating power of the first computer was approximately 2000 operations per second, while previous electro-mechanical devices were capable of performing only 3 or 4 operations. Today’s digital machines can execute more than 1 billion instructions per second. Technological advances and miniaturization techniques have reduced the cost and size of computing machinery.

3.1 Character Representations

Over the years, data representation issues have often been determined by the various conventions used by the different hardware manufacturer. Machines have had different word lengths and different character sets and have used various schemes for storing character and data. Fortunately, in microprocessor and microcontroller design, the encoding of character data has not been subject to major disagreements.

Historically, the methods used to represent characters have varied widely, but the basic approach has always been to choose a fixed number of bits and then map the

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various bit combinations to the various characters. Clearly, the number of bits of the storage format limits the total number of distinct characters that can be represented. In this manner, the 6-bit codes used on a number of earlier computing machines allow representing 64 characters. This range allows including the uppercase letters, the decimal digits, some special characters, but not the lowercase letters.

Computer manufacturers that used the 6-bit format often argued that their customers had no need for lower-case letters. Nowadays 7- and 8-bit codes that allow representing the lower-case letters have been adopted almost universally.

Most of the world (except IBM) has standardized character representations by using the ISO (International Standards Organization) code. ISO exists in several national variants; the one used in the United States is called ASCII, which stands for

American Standard Code for Information Interchange. All microcomputers and microcontrollers use ASCII as the code for character representation.

3.1.1 ASCII

ASCII is a character encoding based on the English alphabet. ASCII was first published as a standard in 1967 and was last updated in 1986. The first 33 codes, referred to as non-printing codes, are mostly obsolete control characters. The remaining 95 printable characters (starting with the space character) include the common characters found in a standard keyboard, the decimal digits, and the upperand lower-case characters of the English alphabet. Table 3.1 lists the ASCII characters in decimal, hexadecimal, and binary.

Table 3.1

ASCII Character Representation

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DIGIT POSITIONAL WEIGHT 27 = 128 26 = 64 25 = 32 24 = 16 23 = 8 22 = 4 21 = 2 20 = 1

0 (LEAST SIGNIFICANT BIT) 1 2 3 4 5 6

7 (MOST SIGNIFICANT BIT)

Figure 3-1 Binary Digit Weights and Numbering

In order to perform arithmetic operations, the digital machine must be capable of storing and retrieving numerical data. Numerical data is stored in standard formats, designed to minimize space and optimize processing. Historically, numeric data was stored in data structures devised to fit the characteristics of a specific machine, or the preferences of its designers. It was in 1985 that the Institute of Electrical and Electronics Engineers (IEEE) and the American National Standards Institute

(ANSI) formally approved mathematical standards for encoding and storing numerical data in digital devices.

The electronic and physical mechanisms used for storing data have evolved with technology. One common feature of many devices, from punched tape to integrated circuits, is that the encoding is represented in two possible states. In paper tape the two states are holes or no holes, while in electronic media they are usually the presence or absence of an electrical charge.

Data stored in processor registers, in magnetic media, in optical devices, or in punched tape is usually encoded in binary. Thus, the programmer and the operator can usually ignore the physical characteristics of the storage medium. In other words, the bit pattern 10010011 can be encoded as holes in a strip of paper tape, as magnetic charges on a mylar-coated disk, as positive voltages in an integrated circuit memory cell, or as minute craters on the surface of the CD. In all cases 10010011 represents the decimal number 147.

3.2.2 Word Size

In electronic digital devices the bistable states are represented by a binary digit, or bit. Circuit designers group several individual cells to form a unit of storage that holds