#
Learning Resources

## Representation of information

**Data Representation**

Character and numbers are understandable and usable by people therefore people feed them to the computer and they expect the result of computation or interaction from computer as output many time in the same form i.e, characters of text of character after processing must appear for them as in English like natural language and processed numbers or results as represented in decimal and in accordance with mathematical notation.

__External Data Representation:__

Natural (English) language characters and decimal numbers are usual be and understandable by the people and termed as External Data Representation. But as such the computer being electronic machine cannot understand and use natural language symbols and decimal numbers directly. External data Representation does not hold good for computations inside the machine.

__Internal Data Representation:__

The internal representation of data inside the computer machine must be acceptable by machine and suit the electronic concepts. This led to the development of separate machine language which is in binary form, consequently the data to be processed must also be in binary form. different methods of representing natural language symbols and decimal numbers in binary form inside the machine constitute, internal data representation.

The characters and numbers are fed to the computer machine and the results produced from the machine, must be in a form that is usable and understandable to the external world; irrespective of internal data representation. The external input to the computer and external output from the computer will normally be natural language symbols and characters, numbers in decimal form.

**Numbering Systems** : The set of symbols and rules that we use to represent quantities, in a numbering system there is an element q is called base, is the number of distinct symbols used to represent a quantity. Is said to be positional when the value of each digit depends on its position in the representation is relative to a base when the value represented by each digit is obtained by multiplying by the power of the base.

1. SNDecimal: Use 10 symbols, positional and relative to a base

2. SNBinario: Uses 2 symbols (0.1) is positional and relative to a base

3. SNOctal: Use eight symbols (0 … 7) is on a positional basis. 1dig = 3dig bina

4. SNHexadecimal: Use 16 symbols (0 … 9, A. .. F) is on a positional basis. 1digHexa = 4díg

**Data Encryption Systems**: A information to be automatically treated needs to be transformed to a code manageable by the computer. The information processed by a computer is presented in a particular representation system that uses an alphabet that incoming calls and through a system of transform coding in a coded information that uses the corresponding output alphabet and will be recognized and treated by computer.

**Numerical Codes**

__1. Pure binary code__ A computer handles data in binary length limitation refers to number of bits and also need to consider the sign to operate with no negatives, the number of digits available is determined by N where N = 8,16,32 … The most common representations:

- Module and a sign: The bit farthest to the left is the sign (0 = positive, 1 = negative), the rest of the bits representing the module no. The range of representation are those n º q can be encoded: 2 ^ N-1 +1

- Complement to a C-1: For positive number as in MS and a negative number is obtained by complementing all the digits, you change the 0 to 1 and vice versa. (0 + and 1 -).

- Complement to two C-2: positive as in MS and C-1 and the negative representation of what we get: We put the number in positive, C-1 and the outcome of the C-1 we add one.

- The codes in excess of 2 ^ N-1: To represent a number in excess to 128, there are q No sumarle to that the number we want to represent and represent it in length to tell us.

- Use of C-1 and C-2: An overflow is when having two number with the same sign out another sign different, if it comes in addition. A carry is the extra one No but I q do is sumárselo the result, if occurs on the addition in C-1 will be rejoining the No. 1 we have taken out, but if it occurs in C-2 is neglected.

__2. Binary Coded Decimal (BCD)__: The BCD uses a quartet for the representation of each decimal place, there are several versions of this code:

- The natural BCD: Each decimal digit is coded by four binary digits.

- – The BCD in excess of 3: Leave three encodings at the beginning and end without representation. Is added to each n º 3.

There are two ways to represent:

- The decimal unpacked: Each decimal digit is represented in two quartets, where the first quartet is all full of one and the second is the figure. The sign of this number is written in the last quartet in place of 1. The only + is 1100 – is 1101.

Eg.1992 1111/0001 1111/1001 1111/1001 1100/0010

1 September 9 + 2

- The packed decimal: Delete the quartet on the left except in the last figure, in this case each quartet has a number in BCD except the last one is the sign. E +1992

1001/1001 0000/0001 0010/1100

0 1 9 9 2 + (plus sign)

__3. Floating Point__: This is used for no very large or very small. Representation is based on scientific notation commonly used in math, in which the amount is represented: Number = Mantissa * Base

- Single precision (32 bits): The first bit is for the sign, the next 8 determine the exponent q is in excess of 128 and the remaining 23 are for the mantissa (binary pure and comes in C-1).

- Double precision (64 bits): The first bit is for the sign, the next 12 are for the exponent, the remaining 51 are for the pure binary mantissa and C-1.

**Alphanumeric codes**: These codes to store and transmit information. Features:

- Is able to represent 10 digits number from 0 to 9, special characters (arithmetic, control, etc), letters, or alphabetic characters (az, AZ).

- The length of a code is the number of bits that is used to represent a character

- Most q character set can represent is 2 ^ length.

**Protective codes and error correction**:

- __Parity Codes__: 1 Error Control bitsañaden to combinations 1bit parity code, looking at the number DE1′s inside combination, including parity. – P. Par-P. Odd

- __Hamming codes__: Control e1bit d errors. Are formed by adding the initial code a number of bits to detect various parities. The set of bits that add as a pure binary number that indicates the position of bit wrong in the absence of error the number would be 0. n bit for the code, add p.

To add must be met: 2 ^ p> = n + p +1