# Code conversion in digital electronics

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 0 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111

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

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

 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