The document discusses different number systems used in computer systems, including decimal, binary, octal, and hexadecimal. It provides details on each system: decimal uses 0-9, binary uses 0-1, octal uses 0-7, and hexadecimal uses 0-9 and A-F. It also describes how to convert between these number systems using methods like repeated division and determining positional value based on the system's base.

1. NUMBER SYSTEM
 Number systems are the technique to
represent numbers in the computer system
architecture, every value that you are saving
or getting into/from computer memory has
a defined number system.

2. TYPES OF NUMBER SYSTEM
 Decimal Number System
 Binary Number System
 Octal Number System
 Hexadecimal Number System

3. Decimal Number System
 The decimal system is composed of 1
numerals or symbols (Deca means 10, that
is why this is called decimal system). These
10 symbols are 0,1,2,3,4,5,6,7,8,9 ; using
these symbols as digit as number, we can
express any quantity. The decimal system,
also called the base-10 system

4. BINARY NUMBER SYSTEM
 Binary System, there are only two symbols
or possible digit values, 0 and 1. This base-2
system can be used to represent any
quantity that can be represented in decimal
or other number systems.
 The Binary system is also a positional-value
system, wherein each binary digit has its
own value expressed as a power of 2.

5. OCTAL NUMBER SYSTEM
 The Octal number system is very important
in digital computer work. The octal number
system has a base of eight, meaning that it
has eight unique symbols : 0,1,2,3,4,5,6,7 .
Thus each digit of an octal number can have
any value from 0 to 7.
 The octal system is a positional value
system, wherein each octal digit has its own
value expressed as a power of 8.

6. HEXADECIMAL NUMBER SYSTEM
 The Hexadecimal System uses base 16.
Thus, it has 16 possible digit symbols. It
uses the digits 0 –9 and the letter A, B, C, D,
E & F as the 16 digit symbols.
 Hexadecimal is a positional value System
has its own value expressed as a power of
16.

7. NUMBER CONVERSIONS
CONVERSIONS WITH BINARY
 Decimal To Binary
 Decimal Fraction To Binary
 Binary To Decimal
 Binary Fraction To Decimal

8. DECIMAL TO BINARY
 To converting decimal to Binary we use Repeated
division method. In this the no. is successively divide
by 2 and its remainder recorded.
 For Example convert decimal to Binary- 4310
CONVERSIONS WITH BINARY

10. DECIMAL FRACTION TO BINARY
 To Convert a decimal fraction into binary,
multiply the decimal fraction by the base
that’s 2. Do until you will get zero at
fractional part.
CONVERSIONS WITH BINARY

11. BINARY TO DECIMAL
 To convert Binary to Decimal, Add
positional weights or values with power of
2 start from right side.
 For Example Convert 11011 to Decimal.
CONVERSIONS WITH BINARY

13. BINARY FRACTION TO DECIMAL
 To find binary fraction, take the sum of
products of each digit value (0 –1) and its
positional value. Starts from left side.
 For Example convert 0.0101 to Decimal.
CONVERSIONS WITH BINARY

14. CONVERSIONS WITH OCTAL
 Decimal To Octal
 Octal To Decimal
 Octal To Binary
 Binary To Octal

15. DECIMAL TO OCTAL
 A decimal integer can be converted to octal
by Repeated division method with division
factor of 8.
 Example Convert 26610 to Octal

17. OCTAL TO DECIMAL
 It can easily converted into decimal by
multiplying each octal digit by its positional
weight.
 For Example 3728 to Decimal

19. OCTAL TO BINARY
 To convert Octal To Binary is easy. This
converting is performed by converting each
octal digit to its 3 bit binary. Possible digits
converted as indicated in Table

20. BINARY TO OCTAL
 Its simply the reverse of octal to binary.
Make the three bits group starting from left
side. Then convert it with using Table

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