Computer Architecture : Data Representation in Computers

Data Representation refers to the methods used internally to represent information stored in a computer. Computers store lots of different types of information: for example numbers, text, graphics, sound etc. However, ALL types of information stored in a computer are stored internally in the same simple format, BINARY form : a sequence of 0's and 1's.

Modern computers are built up with transistors. Whenever an electric current pass into the transistors either an ON or OFF status will be established. Therefore the computer can only recognize two numbers, 0 for OFF, and 1 for ON, which can be referred to as BIT. There is nothing in between Bit 0 and Bit 1.  Hence computers can be said to be discrete machines. The number system consists only of two numbers is called Binary System. And to distinguish the different numbering systems, the numbers human use, ie 1,2,3,4..., will be called Decimals (since they are based 10 numbers) from now on.

Binary Numbers

Normally we write numbers using digits 0 to 9. This is called base 10. However, any positive integer (whole number) can be easily represented by a sequence of 0's and 1's. Numbers in this form are said to be in base 2 and they are called binary numbers. Base 10 numbers use a positional system based on powers of 10 to indicate their value. The number 123 is really 1 hundred + 2 tens + 3 ones. The value of each position is determined by ever-higher powers of 10, read from left to right. Base 2 works the same way, just with different powers. The number 101 in base 2 is really 1 four + 0 twos + 1 one (which equals 5 in base 10).


Text can be represented easily by assigning a unique numeric value for each symbol used in the text. For example, the widely used ASCII code (American Standard Code for Information Interchange) defines 128 different symbols (all the characters found on a standard keyboard, plus a few extra), and assigns to each a unique numeric code between 0 and 127. In ASCII, an "A" is 65," B" is 66, "a" is 97, "b" is 98, and so forth. When you save a file as "plain text", it is stored using ASCII. ASCII format uses 1 byte per character 1 byte gives only 256 (128 standard and 128 non-standard) possible characters The code value for any character can be converted to base 2, so any written message made up of ASCII characters can be converted to a string of 0's and 1's.


Graphics that are displayed on a computer screen consist of pixels: the tiny "dots" of color that collectively "paint" a graphic image on a computer screen. The pixels are organized into many rows on the screen. In one common configuration, each row is 640 pixels long, and there are 480 such rows. Another configuration (and the one used on the screens in the lab) is 800 pixels per row with 600 rows, which is referred to as a "resolution of 800x600." Each pixel has two properties: its location on the screen and its color. A graphic image can be represented by a list of pixels. Imagine all the rows of pixels on the screen laid out end to end in one long row. This gives the pixel list, and a pixel's location in the list corresponds to its position on the screen. A pixel's color is represented by a binary code, and consists of a certain number of bits. In a monochrome (black and white) image, only 1 bit is needed per pixel: 0 for black, 1 for white, for example. A 16 color image requires 4 bits per pixel. Modern display hardware allows for 24 bits per pixel, which provides an astounding array of 16.7 million possible colors for each pixel.

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