Digital Logic Fundamentals, Numbering System, Octal to Hexadecimal and Hexadecimal to Octal

1. NUMBER SYSTEM CONVERSION
Dr.S.ANITHA
Octal to Hexadecimal & Hexadecimal to Octal
There is no direct conversion between octal to hexadecimal and hexadecimal to octal.
It can be done via decimal or binary. But, via binary is easier.
Octal to Hexadecimal
1. Octal to Binary
2. Binary to Hexadecimal
(765)8 = ()16
Octal
(0-7)
Binary (3 digits)
22
21
20
4 2 1
0 0 0 0
1 0 0 1
2 0 1 0
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1

2. 1. Octal to Binary
(765)8 = 111 110 101
2. Binary to Hexadecimal
111110101
111110101 (Group four digits)
000111110101 (add zero at left side to make it as 4 digits)
000111110101
1 15 5
(765)8 = (1F5)16
*****
(653)8 =()16 = 1AB
(754.32)8 =()16 = 1EC.68
000111 101 100 . 011 01000
1 14 12 . 6 8
1EC . 68
Hexadecimal to Octal
1. Hexadecimal to Binary
2. Binary to Octal

3. (F5A)16 = ()8
1. Hexadecimal to Binary
F5A
F  1111
5  0101
A  1010
( 111101011010)2
2. Binary to Octal
421
( 111101011010)2
(7532)8
(F5A)16 = (7532)8
**********
(D9A)16 = ()8 = 6632
(BF4.C1)16 = ()8 = 5764.602
*****

4. 1’s complement  invert 1’s and 0’s
2’s complement  1’s complement + 1
1’s complement
10110  01001
2’s complement
1
10110  01001
1
_______________
0 1 0 1 0
010101  101010 (1’s complement)
101011 (2’s Complement)