# Data representation and Number system

Last updated on November 12th, 2018

**Data representation: **Data and commands cannot be keyed and managed on a computer using human-legible language. Any form of data is it letters and numbers, sound or pictures or symbols are essentially transformed into machine-legible / binary form. For this aim, it is significant to comprehend how a computer with the aid of its peripheral devices holds data in its circuits, magnetic devices, and optical media.

**Data representation in digital circuits:** This is electronic parts, such as microprocessors, consisting of millions of circuits. The accessibility of high voltage (on) in these circuits is deduced as ones while an off(low voltage)deduced as zeros.

**Data representation on optical media:** In optical media, the existence of light is deduced as ones while its lack is deduced as zeros. Optical devices use this technology to store and read data. For instance, when a Compact Disc (CD/DVD) is viewed under a powerful microscope the glossy film is detected to have very tiny pocket holes called **pits** while the areas that don’t have pocket holes are called **land**.

**Data representation on magnetic media**: A laser beam mirrored from the pocket holes are read, as one. The laser arriving in the pot is not reflected thus deduced as zero. The mirrored design of light from the revolving disk falls on a photoelectric sensor that alters the patterns into digital form. A perfect example of this is a hard disk.

**Number system and their representation: **

These are sets of symbols used to characterize the values resulting from a common base or radix. Number systems are classified into:

**Decimal number system**: derived from the Latin prefix Deci, which means ten, this system has ten digits ranging from 0-9. Also called a base 10 number system or ordinary number system, it must always be inscribed with a subscript 10 e.g. X_{10. }The magnitude of a figure can be measured using the following parameters:

- The absolute value is the magnitude of a digit in a number
- The place value of a digit in a number is the position of the digit in that number for example whether hundreds.
- The total value of a number is the totality of the place value of every digit making the number.
- The base value of a number also referred to as the radix, hinges on the type of the number systems used.

- The
**Binary number system**uses two digits namely, Ones and Zeros represent numbers. As opposed to decimal numbers with a place value raised by a factor of ten, in a binary system, the place values escalation by the factor of two. Binary numbers are expressed as X_{2}. consider a binary number such as 1011_{2}. The rightmost digit has a place value of 1×2^{0}while the leftmost has a place value of 1×2^{3}. **An Octal number system c**ontains eight digits ranging from 0-7 and the place value of octal numbers raises in factors of eight from right to left.**Hexadecimal number system,**this is a system that consists of 16 digits ranging from 0-9 and letters A-F, where A is the same as 10, B as 11 all the way to F which corresponds to 15 in base ten system. The place value of hexadecimal numbers increases by factors of sixteen.