number system 2

	Code Conversion
		Converting from one code form to another code form is called code conversion, like converting from binary to decimal or converting from hexadecimal to decimal.
		Binary-To-Decimal Conversion
		Any binary number can be converted to its decimal equivalent simply by summing together the weights of the various positions in the binary number which contain a 1.
		Binary Decimal 110112 24+23+01+21+20 =16+8+0+2+1 Result 2710
		and
		Binary Decimal 101101012 27+06+25+24+03+22+01+20 =128+0+32+16+0+4+0+1 Result 18110
		You should have noticed that the method is to find the weights (i.e., powers of 2) for each bit position that contains a 1, and then to add them up.
		Decimal-To-Binary Conversion
		There are 2 methods:
		Reverse of Binary-To-Decimal Method Repeat Division
		Reverse of Binary-To-Decimal Method
		Decimal Binary 4510 =32 + 0 + 8 + 4 +0 + 1 =25+0+23+22+0+20 Result =1011012
		Repeat Division-Convert decimal to binary
		This method uses repeated division by 2.
		Convert 2510 to binary
		Division Remainder Binary 25/2 = 12+ remainder of 1 1 (Least Significant Bit) 12/2 = 6 + remainder of 0 0 6/2 = 3 + remainder of 0 0 3/2 = 1 + remainder of 1 1 1/2 = 0 + remainder of 1 1 (Most Significant Bit) Result 2510 = 110012
		The Flow chart for repeated-division method is as follows:
		Binary-To-Octal / Octal-To-Binary Conversion
		Octal Digit 0 1 2 3 4 5 6 7 Binary Equivalent 000 001 010 011 100 101 110 111
		Each Octal digit is represented by three binary digits.
		Example:
		100 111 0102 = (100) (111) (010)2 = 4 7 28
		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)