1.1 Data representation in a computer  (Page 3/6)

After that, multiply the fractional part by b repeatedly to get each digit as an integer part. We will continue this process until we get a zero as our fractional part or until we recognize an infinite repeating pattern.

Now convert 0.625 to hexadecimal :

.

0.39625 * 16 = 0.625 ------------------------------------->0

.625* 16 = 10 --------------------------->A.

We get fractional part is zero.

In summary, the result of conversion ${43868.39625}_{(10)}$ to hexadecimal is AB5C.0A

Data representation in a computer. units of information

Basic principles

Data Representation refers to the methods used internally to represent information stored in a computer. Computers store lots of different types of information:

• numbers
• text
• graphics of many varieties (stills, video, animation)
• sound

At least, these all seem different to us. However, all types of information stored in a computer are stored internally in the same simple format: a sequence of 0's and 1's. How can a sequence of 0's and 1's represent things as diverse as your photograph, your favorite song, a recent movie, and your term paper?

• Numbers must be expressed in binary form following some specific standard.
• Character data are assigned a sequence of binary digits
• Other types of data, such as sounds, videos or other physical signals are converted to digital following the schema below

Digital signal

Continuous signalPhysical signalComputerConvert ADSensor

Depending on the nature of its internal representation, data items are divided into:

• Basic types (simple types or type primitives) : the standard scalar predefined types that one would expect to find ready for immediate use in any programming language
• Structured types(Higher level types) are then made up from such basic types or other existing higher level types.

Units of information

The most basic unit of information in a digital computer is called a BIT, which is a contraction of Binary Digit. In the concrete sense, a bit is nothing more than a state of "on" or "off" (or "high" and "low") within a computer circuit. In 1964, the designers of the IBM System/360 mainframe computer established a convention of using groups of 8 bits as the basic unit of addressable computer storage. They called this collection of 8 bits a byte.

Computer words consist of two or more adjacent bytes that are sometimes addressed and almost always are manipulated collectively. The word size represents the data size that is handled most efficiently by a particular architecture. Words can be 16 bits, 32 bits, 64 bits, or any other size that makes sense within the context of a computer's organization.

Some other units of information are described in the following table :

Representation of Integers

An integer is a number with no fractional part; it can be positive, negative or zero. In ordinary usage, one uses a minus sign to designate a negative integer. However, a computer can only store information in bits, which can only have the values zero or one. We might expect, therefore, that the storage of negative integers in a computer might require some special technique - allocating one sign bit (often the most significant bit) to represent the sign: set that bit to 0 for a positive number, and set to 1 for a negative number.