(i) There are two procedures for converting from decimal to binary.
(ii) They are
Expansion Method
Repeated division by 2.

A decimal number system is the frequently used number system.

Each successive number after 7 is a combination of 2 or more unique symbols of Octal system

The radix of Decimal is 10, Binary is 2, Octal is 8 and Hexadecimal is 16

(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.

The most popular way of representing negative numbers in computer systems is two's complement. The advantages of using this method are :
(i) There are no two ways of representing a zero as in the case with the above two methods.
(ii) Addition and subtraction can be performed effectively

In computer technology, there are three common ways of representing a signed Binary number.
(i) Prefixing an extra sign bit to a Binary number.
(ii) Using one's complement.
(iii) Using two's complement

(365)₈ = 3 x 8² x 6 x 8¹ + 5 x 8^{0
            =} 192 + 48 + 5 = (245)₁₀
(366)₈ = 3 x 8² + 6 x 8¹ + 6 x 8⁰
          = 192 + 42 + 6 = (246)₁₀
(367)₈ = 3 x 8² + 6 x 8¹ + 7 x 8⁰
         = 192 + 42 + 6 = (247)₁₀
In decimal form, the given sequence will be 245, 246, 247, 248, 249, 250. To complete the sequence of Octal number, we need to find the octal equal of 248, 249 and 250

(COFFEE)₁₆
\(\overset { C }{ \underset { 1100 }{ \downarrow } } \)\(\overset { O }{ \underset { 0000 }{ \downarrow } } \)\(\overset { F }{ \underset { 1111 }{ \downarrow } } \)\(\overset { F }{ \underset { 1111 }{ \downarrow } } \)\(\overset { E }{ \underset { 1110 }{ \downarrow } } \)\(\overset { E }{ \underset { 1110 }{ \downarrow } } \)
(COFFEE)₁₆  = (110000001111111111101110)₂

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 fon only and the computer is then expected to convert the decimal number to other number systems which it understands.

(101.10)₁₆ in binary From 
               = 1       0       1       1       0
                  0001  0000  0001  0001  0000
(101.10)₂ = (000100000001.00010000)₂
(101.10)₁₆  in Decimal Form
(101.10)₂  = 1 x 16² + x 16¹ + 1 x 16⁰ + 1 x 16^-1 + 0 x 16^-2
               = 256 + 0 + 1 + 0.0625 + 0 =(275.0625)₁₀  

Steps for Decimal to Binary Conversion.
Step 1: Divide the decimal number which is to be converted by two which is the base of the binary number.
Step 2: The remainder which is obtained from step 1 is the least significant bit of the new binary number.
Step 3: Divide. the quotient which is obtained from the step 2 and the remainder obtained from this is the second least significant bit of the binary number
Step 4: Repeat the process until the quotient becomes zero.
Step 5: The last remainder obtained from the division is the most significant bit of the binary number. Hence, arrange the number from the most significant bit to the least significant bit (i.e., from bottom to top).