Repeat Division-Convert decimal to octal

This method uses repeated division by 8

Example: Convert 177₁₀ to octal and binary

Division	Result	Binary
177/8	= 22+ remainder of 1	1 (Least Significant Bit)
22/ 8	= 2 + remainder of 6	6
2 / 8	= 0 + remainder of 2	2 (Most Significant Bit)
Result	17710	= 2618
Binary		= 0101100012

Hexadecimal to Decimal/Decimal to Hexadecimal Conversion
Example:
2AF₁₆ = 2 x (16²) + 10 x (16¹) + 15 x (16⁰) = 687₁₀

Repeat Division- Convert decimal to hexadecimal

This method uses repeated division by 16.

Example: convert 378₁₀ to hexadecimal and binary:

Division	Result	Hexadecimal
378/16	= 23+ remainder of 10	A (Least Significant Bit)23
23/16	= 1 + remainder of 7	7
1/16	= 0 + remainder of 1	1 (Most Significant Bit)
Result	37810	= 17A16
Binary		= 0001 0111 10102

Binary-To-Hexadecimal /Hexadecimal-To-Binary Conversion

Hexadecimal Digit	0	1	2	3	4	5	6	7
Binary Equivalent	0000	0001	0010	0011	0100	0101	0110	0111

Hexadecimal Digit	8	9	A	B	C	D	E	F
Binary Equivalent	1000	1001	1010	1011	1100	1101	1110	1111

Each Hexadecimal digit is represented by four bits of binary digit.
Example:
1011 0010 1111₂ = (1011) (0010) (1111)₂ = B 2 F₁₆

Octal-To-Hexadecimal Hexadecimal-To-Octal Conversion

• Convert Octal (Hexadecimal) to Binary first.
• Regroup the binary number by three bits per group starting from LSB if Octal is required.
• Regroup the binary number by four bits per group starting from LSB if Hexadecimal is required.

Example:
Convert 5A8₁₆ to Octal.

Hexadecimal	Binary/Octal
5A816	= 0101 1010 1000 (Binary)
	= 010 110 101 000 (Binary)
Result	= 2 6 5 0 (Octal)

Binary Codes
Binary codes are codes which are represented in binary system with modification from the original ones. Below we will be seeing the following:

• Weighted Binary Systems
• Non Weighted Codes

Weighted Binary Systems
Weighted binary codes are those which obey the positional weighting principles, each position of the number represents a specific weight. The binary counting sequence is an example.

Decimal	8421	2421	5211	Excess-3
0	0000	0000	0000	0011
1	0001	0001	0001	0100
2	0010	0010	0011	0101
3	0011	0011	0101	0110
4	0100	0100	0111	0111
5	0101	1011	1000	1000
6	0110	1100	1010	1001
7	0111	1101	1100	1010
8	1000	1110	1110	1011
9	1001	1111	1111	1100

8421 Code/BCD Code
The BCD (Binary Coded Decimal) is a straight assignment of the binary equivalent. It is possible to assign weights to the binary bits according to their positions. The weights in the BCD code are 8,4,2,1.

Example: The bit assignment 1001, can be seen by its weights to represent the decimal 9 because:
1x8+0x4+0x2+1x1 = 9