2.5 Bit Strings and Their Meaning

As discussed before, the contents of the memory consist of strings of bits. Most computers have these stored in individually addressable units of eight bits, called bytes. The bytes in turn can be strung together to form longer strings. For historical reasons, a group of two consecutive bytes is called a half word, four bytes (32 bits) are called a word, and 64 bytes are called a double or long word.

The meaning of the strings of bits is just that—a string of bits. The interpretation of the meaning, however, is dependent on the usage of the string. One important usage is to code an instruction and its parameters. There are many types of instructions: numerical, like add and multiply, logical, control, program flow, and others. Again, this book is not devoted to hardware details, so we do not elaborate. Simply said, a string of bits can be interpreted as an instruction, and given the address of the proper byte in this string, the control unit will try to decode and execute that instruction. The instruction itself will cause the control unit to find the next instruction, and so on.

Bit strings also can represent data. Here we have a wide variety of possibilities, so we restrict ourselves to the most prevalent data coding.

The simplest one is the integer. In this interpretation, the bit string represents a positive numerical value in radix 2. This means that each string represents a binary number, where each digit is weighed by the proper power of two, starting from zero on the extreme right (end of the string) and proceeding to the left. Thus, the string 01011101 will have the meaning 1 × 2⁰ + 0 × 2¹ + 1 × 2² + 1 × 2³ + 1 × 2⁴ + 0 × 2⁵ + 1 × 2⁶ + 0 × 2⁷, where × is the multiplication sign. Evaluating this expression, the string 01011101 has the value of 1 + 0 + 4 + 8 + 16 + 0 + 64 + 0 or 93. We do not discuss here how negative values are represented, but they are available.

Integer values are limited by the length of their string representations. Ruby recognizes two types of integers: regular and long. We discuss those (and other numeric representations) and their properties in a forthcoming chapter.

To alleviate the limitation of size imposed on integers, a very important representation of data is available. It is called floating point or real. The former name is older and used primarily in discussing hardware concepts.

In this interpretation, numbers are represented in scientific form, that is, as x × 2^y. Thus, part of the string is used to hold the value of x and part is used to hold the value of y. Both x and y are expressed by their binary values, derived in the same way that we presented in our discussion of integers, or in a complex form as negative values introduce additional difficulties. As you will see, there are different types of real numbers.

The last interpretation that we discuss is that of characters.

Character representation follows an international standard, codified under the name Unicode. The standard provides for a representation of both character and noncharacter-based texts (such as, for example, Far East languages) and for the representation of other items (such as, for example, mathematical symbols, control characters, etc.). The Unicode representation uses one to four bytes per item. The first 256 characters, digits, symbols, and codes are contained in one byte and are identical to the previous standard known as ASCII (American Standard for Character Information Interchange). Almost all English-based texts files belong to this category, so it is customary to state that characters are single bytes.

For in-depth information on this important topic, the voluminous Unicode standard description (currently more than 600 pages) contains tables, descriptions, rules, and explanations for dozens of different scripts, languages, symbols, and so on.

There is a difference between character representations and their meaning. For example, the character “9” is not the number 9. The number 9 is represented by the character “9.” This distinction will be very important in future chapters as we have input programs that read characters, but we wish to use them as numbers. In our former example, we have seen that the number 93 is stored as the string 01011101, but the character string “93” will be stored in a completely different way. To obtain the number 93 from the character string “93,” we need a process of conversion from the character to the numerical representation. Ruby provides such a process, as do all programming languages.

These are the most important but by no means the only types of interpretations of bit strings. Some others may represent different types of data, be they components of colors for the display, controls for various devices, amplitudes for sound presentation, and so on.