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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

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)