The document discusses different number systems including binary, octal, decimal, and hexadecimal. It provides details on their bases, the digits used in each system, and methods for converting between the different number systems. Conversions can be done directly between binary, octal, and hexadecimal without having to first convert to decimal.

1. NUMBER SYSTEM
Binary, Octal, Decimal and Hexadecimal

2. NUMBER SYSTEM
Number System Base Digits/Alphabets used
Binary 2 0,1
Octal 8 0,1,2,3,4,5,6,7
Decimal 10 0,1,2,3,4,5,6,7,8,9
Hexadecimal 16 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
A = 10, B = 11, C = 12, D = 13,
E = 14, F = 15

3. DECIMAL NUMBER SYSTEM

4. DECIMAL NUMBER SYSTEM

5. BINARY NUMBER SYSTEM

6. OCTAL NUMBER SYSTEM

7. HEXADECIMAL NUMBER SYSTEM

8. CONVERSION FROM BINARY, OCTAL AND
HEXADECIMAL TO DECIMAL NUMBER SYSTEM

9. CONVERSION OF OCTAL TO DECIMAL
CONVERSION OF HEXADECIMAL TO DECIMAL

10. CONVERSION FROM DECIMAL TO BINARY, OCTAL
AND HEXADECIMAL

11. DECIMAL TO BINARY

12. DECIMAL TO OCTAL

13. DECIMAL TO HEXADECIMAL
The conversion method of decimal to hexadecimal is the same as that of decimal to binary except
that the base taken is 16 instead of 2.
For example, to convert 765.24510 to the hexadecimal equivalent, do the following:
Integer Part Fractional Part
16 765
16 47 - 13
16 2 - 15
0 - 2
0.245
x 16
3.920
x 16
14.720
x 16
11.520
765.24510 = 2FD.3EB16

14. DIRECT CONVERSION – YOU CAN DO DIRECT CONVERSIONS AMONG
BINARY, OCTAL AND HEXADECIMAL NUMBERS.

15. BINARY TO OCTAL

16. HEXADECIMAL
TO BINARY – YOU
CAN CONVERT A
HEXADECIMAL
NUMBER TO ITS
BINARY
EQUIVALENT
AND VICE VERSA
DIRECTLY, AS
EACH
HEXADECIMAL
DIGIT IS
EQUIVALENT TO
FOUR BINARY
DIGITS.
1010101100010010.011110002

17. BINARY TO HEXADECIMAL