Hexadecimal or base 16 number systems having 16 possible symbols, the decimal symbols 0 through 9 are used up and the letters A through F for values 10 through 15. This number system is often called Hex code.
The digit values for hexadecimal and symbols for hex code is as follows in fig. (a) and fig. (b) resp.
A E 6 . 7 6
162 161 160 16-1 16-2
Hex symbols is as follows
Decimal Hex
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F
Conversion from Binary Number system to Hex-decimal number system
1. Write down binary number separately
2. Mark off the binary digits in groups of four from right to left.
3. Each group of four binary digits is equal to one Hex digit.
4. Each hex digit is equal to four binary digits.
Example1: (101101110001)2 = (?)16 or Hex
Binary: 1011 0111 0001
Hex B 7 1
Hence (101101110001)2 = (B71)16 or Hex
Example1: (110110110110)2 = (?)16 or Hex
Binary: 1101 1011 0110
Hex D B 6
Hence (101101110001)2 = (DB6)16 or Hex
Conversion from Hex to Binary
Example: (ADE6) H = (?)2
Hex: A D E 6
Binary: 1010 1101 1110 0110
And Hence (ADE6)H = (1010110111100110)2
Conversion from octal to hex and vice versa
To convert from octal to hex code, the easiest way is to write the binary equivalent of the octal and then convert the binary digits, four at a time, into the appropriate hex digits. Reverse the procedure to get from hex to octal.
Example 1: (537)8 = (?)H
Octal: 5 3 7
Binary: 101 011 111
0001 0101 1111
Hex: 1 5 F
And hence (537)8 = (15F) H
Example 2: (D6) H = (?)8
Hex: D 6
Binary: 1101 0110
011 010 110
Octal: 3 2 6
And hence (D6) H = (326)8
Conversion from Decimal to Hexadecimal and Vice Versa
1. Divide the decimal number by 16
2. Keep remainder and quotient aside.
3. Again Divide this quotient by 16 and keep remainder and quotient aside.
4. Repeat this procedure until the quotient reaches zero.
5. The column of remainders will be the hex equivalent of the given decimal number.
6. The MSB is on the bottom of the column.
7. The LSB is on the top of the column.
Example 1: (227)10 = (?)H
14 3
Hex code: E 3
Hence (227)10 = (E3)H
Example 2: (DB4)H = (?)10
Hex Code: D B 4
13 11 4
= (13*162) + (11*161) + (4*160)
=(13 * 256) + (11 *16) + (4 *1)
= 3328 + 176 + 4
= 3508
And hence (DB4)H = (3508)10
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