# Assignment 1 - Data Representation

Topics: Binary numeral system, Hexadecimal, Decimal Pages: 6 (1745 words) Published: January 30, 2013
Produce a leaflet for a trainee programmer which explains the following: Why the knowledge of the binary numbering system is essential * The binary numbering system plays a central role in how information of all kinds is stored on the computer. Understanding binary can lift a lot of the mysteries from computers because at a fundamental level they're really just machines for flipping binary digits on and off. There are several activities on binary numbers in this document, all simple enough that they can be used to teach the binary system to anyone who can count! Generally children learn the binary system very quickly using this approach, but we find that many adults are also excited when they finally understand what bits and bytes really are. * How binary numbers can represent decimal numbers

* In mathematics and computer science, the binary numeral system, or base 2, represents numeric values using two digits 0 and 1. The 0 and 1 is the off and on states of the switches with 0 being the off state. Because of its straightforward implementations in electronic circuitry using logic gates the binary system is used internally by all modern computers and computer based devices like mobile phones. Any number can be represented by a sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following sequence of 1s and 0s is interpreted as the binary numeric value of 667: 1 0 1 0 0 1 1 0 1 1. The numeric value represented in each case is dependent upon the value assigned to each symbol. In a computer, the numeric values may be represented by two different voltages; on a magnetic disk, magnetic polarities may be used. A "positive", "yes", or "on" state is not necessarily equivalent to the numerical value of one; it depends on the architecture in use. * Why hexadecimal is a useful numbering system

* A big problem with the binary system is verbosity. To represent the value 202 requires eight binary digits. The decimal version requires only three decimal digits and, thus, represents numbers much more compactly than does the binary numbering system. This fact was not lost on the engineers who designed binary computer systems. When dealing with large values, binary numbers quickly become too unwieldy. The hexadecimal (base 16) numbering system solves these problems. Hexadecimal numbers offer the two features: * hex numbers are very compact

* It is easy to convert from hex to binary and binary to hex. * The Hexadecimal system is based on the binary system using a Nibble or 4-bit boundary. In Assembly Language programming, most assemblers require the first digit of a hexadecimal number to be 0, and place an "h" at the end of the number to denote the number base. * How text can be represented in a computer system

* The ASCII text-encoding standard uses 128 unique values (0–127) to represent the alphabetic, numeric, and punctuation characters commonly used in English, plus a selection of control codes which do not represent printable characters. For example, the capital letter A is ASCII character 65, the numeral 2 is ASCII 50, the character} is ASCII 125 and the metacharacter carriage return is ASCII 13. Systems based on ASCII use seven bits to represent these values digitally. In contrast, most computers store data in memory organized in eight-bit bytes. Files that contain machine-executable code and non-textual data typically contain all 256 possible eight-bit byte values. Many computer programs came to rely on this distinction between seven-bit text and eight-bit binary data, and would not function properly if non-ASCII characters appeared in data that was expected to include only ASCII text. For example, if the value of the eighth bit is not preserved, the program might interpret a byte value above 127 as a flag telling it to perform some function. It is often desirable, however, to...