(i) Decimal Number system
(ii) Binary Number system
(iii) Octal Number system
(iv) Hexadecimal Number system

The decimal Number system is the number system used in general.

(i) Numbers
(ii) Text
(iii) Graphics
(iv) Animations
(v) Audio
(vii) Video etc

(46)₁₀ into Binary = 101110₂

Step 1: Convert given Decimal number into Binary
Step 2: Check if the binary number contains 8 bits if less add 0 at the left most bit, to make it as 8 bits.
Step 3: Invert all bits (i.e. Change 1 as 0 and 0 as 1).

The term data comes from the word datum, which means a raw fact. The data is a fact about people. places or some objects.
Example : Rajesh 16, XI

101010₂
= 0010  0010
= 2        10
= 2        A
(101010)₂ = (2A)₁₆
(101010)₂ = (1 x 2⁵) + ( 0 x 2⁴) + (1 x 2³) + (0 x 2²) + ( 1x 2¹) + (0 x 2⁰)
= 32 + 0 + 8 + 0 + 2 + 0 = 42₁₀ 
(101010)₂ = (2A)₁₆ = 42₍₁₀₎

The number conversion is necessary because us enters the data into the computer in decimal form only and the computer is then expected to convert the decimal number to other number systems which it understands.

8 bit Format of 20₁₀  = 00010100
8 bit format of 25₁₀   = 00011001
20₁₀ + 25₁₀              = _________
                                   00101101
                                   __________
20₁₀ + 25₁₀ = 00101101₂

ISCII - Indian Standard Code for Information Interchange (ISCII) is the system of handling the character of Indian local languages. This is a 8-bit coding system. Therefore it can handle 256 (28) characters. It is recognized by Bureau of Indian Standards (BIS). It is integrated with unicode.
The supported scripts are:
Assamese, Bengali (Bangla), Devanagari, Gujarati, Gurmukhi, Kannada, Malayalam, Oriya, Tamil, and Telugu. ISCII does not encode the writing systems of India based on Arabic, but its writing system switching codes none the less provide for Kashmiri, Sindhi, Urdu, Persian, Pashto and Arabic. The Arabic-based writing systems were subsequently encoded in the PASCII encoding.
ISCII is an 8-bit encoding. The lower 128 code points are plain ASCII, the upper 128 code points are ISCII-specific. In addition to the code points representing characters, ISCII makes use of a code point with mnemonic ATR that indicates that the following byte contains one of two kinds of information. One set of values changes the writing system until the next writing system indicator or end-of-line.

Change it to Binary

150₁₀ = 10010110₂
Step 2 : Change it to Octal
10,010,110
421 421 421
010 010 110
Binary 10010110₂
Octal =226₈

In Binary Number System, there are only two digits namely 0 and 1. The numbers in the binary system are represented to the base 2. In the Binary Number, the left most bit is the Most Significant Bit (MSB) and the right most bit is the Least Significant Bit (LSB). MSB has largest positional weight and LSB has smallest positional weight.
Ex. 110010₂

(i) Unicode is the newest concept in digital coding. In Unicode, every number has a unique character.
(ii) Unicode is the universal character encoding standard used for the representation of text for computer processing
(iii) It can be used to store and process all significant current and past languages. Unicode provides a unique hex encoded number for every character
(iv) Unicode is a 16-bit code, which allows for about 65,000 different representations. This is enough to encode the popular Asian languages (Chinese, Korean, Japanese, etc.)
(v) It also turns out that ASCII codes are preserved. Therefore, conversion between ASCII and Unicode is a simple method (take all one byte ASCII codes and zero-extend them to 16 bits).
(vi) This will be the Unicode version of the ASCII characters. The C, C++ programs use the ASCII Code, and Java programs have already used Unicode. The Unicode Standard has been adopted by industry leaders such as Apple, HP, IBM, Microsoft, Oracle, SAP, Sun, Sybase, and Unisys. Unicode is required by web users and modem standards.

The logic gates like NAND, NOR, XOR and XNOR are derived gates which are derived from the fundamental gates AND, OR NOT.
(1) NAND gate:
The NAND is the combination of NOT and AND. The NAND is generated by inverting the output of an AND operation.
Output: y = \(\overline { \left( A.B \right) } \)

The truth table for NAND gate is

(ii) NOR gate:
The NOR is the combination of NOT and OR. The NOR is generated by inverting the output of an OR operation.
Logic function: y = \(\overline { \left( A+B \right) } \)

the truth table for NAND gate is

(iii) XOR gate:
The XOR (exclusive - OR) gate acts in the same way as the logical either /or.

the truth table 

(iv) XNOR gate:
XNOR (exclusive - NOR) gate is a combination of XOR gate followed by an inverter.
Logic function: y= \(\overline { A \ B } \)

the truth table 

Boolean function:
\(\mathrm{C} =\overline{\mathrm{A} \oplus \mathrm{B}} \)
\(=\overline{{\overline{\mathrm{A}}} \cdot \mathrm{B}+\mathrm{A} \cdot \overline{\mathrm{B}}} \)
\(=\overline{\overline{\mathrm{A}} \cdot \mathrm{B}} \cdot \overline{\mathrm{A} \cdot \overline{\mathrm{B}}} \)
\(=(\overline{\mathrm{A}}+\overline{\mathrm{B}})(\overline{\mathrm{A}}+\overline{\bar{B}}) \)
\(=(\mathrm{A}+\overline{\mathrm{B}})(\overline{\mathrm{A}}+\mathrm{B}) \)
\(=\mathrm{A} \overline{\mathrm{A}}+\overline{\mathrm{AB}}+\mathrm{AB}+\mathrm{B} \overline{\mathrm{B}}  \quad \mathrm{A \overline {A }}=\mathrm{O}\)
\(\mathrm{C} =\overline{\mathrm{A}} \overline{\mathrm{B}}+\mathrm{AB}\)