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NUMBER SYSTEMTHE FOLLOWING PPT COVERS THE FOLLOWING THINGS: INTRODUCTION WHAT IS A DECIMAL
NUMBER? WHAT IS A BINARY
NUMBER? conversion of binary to
decimal and vice-versa conversion of octal to
decimal and vice-versa
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INTRODUCTIONA number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16 and (52)8 both refer to the same quantity, (42)10, but their representations are different.
A binary number is a number that includes only ones and zeroes.
Another name for binary is base-2 ( "base two") .
Computers store information using binary numbers
It is the building block of all dataIn order to understand storage capacity and sizes, you need to know how data is read and saved
In Binary we count in the opposite direction 8421.
What is a binary number?
=
1. The first position value is 20 , i.e. one2. The 2nd position value is 21 , i.e. two3. The 2nd position value is 22 , i.e. four4. The 2nd position value is 23 , i.e. eight5. The 2nd position value is 24 , i.e.
sixteen etc.
CONVERSION OF BINARY
TO DECIMAL
The value of binary 01100001 is decimal 105. This is worked out below:
----------------------------------------------------------------------0 1 1 0 1 0 0 1
1 X 1 = 10 X 2 = 00 X 4 = 01 X 8 = 80 X 16 = 01 X 32 = 321 X 64 = 64
0 X 128 = 0----Answer: 105
EXAMPLE
7
The numbers that we are used to seeing are called decimal numbers.
Decimal numbers consist of the digits from 0 (zero) through 9.
Another name for decimal numbers are base-10 (pronounced "base ten") numbers.
WHAT IS A DECIMAL NUMBER?
8
S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
CONVERSION OF DECIMAL TO BINARY
What is octal number ? Octal digits have place values based on
the value 8. The octal numbering system includes
eight base digits ( 0, 1, 2, 3, 4, 5, 6, 7 ) Computer scientists are often looking for
shortcuts to do things. One of the ways in which we can
represent binary numbers is to use their octal equivalents instead.
This is especially helpful when we have to do fairly complicated tasks using numbers.
CONVERSION OF OCTAL TO DECIMAL
NUMBER 1. In the number 111 base 8, the digit farthest to the right is in the “ones” place and is worth 1. Technically this is the 80
place.2. The 2nd digit from the right, 111, is in the “eights” place, the
“base” place, and is worth 8. Technically this is the 81 place.3. The 3rd digit from the right, 111, is in the “sixty-fours” place,
the “base squared” place, and is worth 64.Technically this is the 82 place.
The total value of this octal number, 111, is 64+8+1, or seventy-three.
Example: convert the number 111,base 10 to octal.
Conversion of decimal to binary
738
9
1
8
1
17310 = 1118
CONVERSION OF BINARY
TO OCTAL The conversion between binary and octal is quite simple. Since 2 to the power of 3 equals 8, it takes 3 base 2 digits to
combine to make a base 8 digit. 000 base 2 equals 0 base 8
0012 = 18
0102 = 28
0112 = 38
1002 = 48
1012 = 58
1102 = 68
1112 = 78
What if you have more than three binary digits, like 110011?
Just separate the digits into groups of three from the right, then convert each group into the corresponding base 8 digit.
110 011 base 2 = 63 base 8 1100101 = 1 100 101 = 001 100 101
THANK YOU
PRESENTED BY GROUP-6
RISHABH KANTH - PPT SHRIYA PARASHAR SUBHAM LUTHRA SAKSHAM SUNDRANI SANIDHYA KHATRI SHLOK AGRAWAL
MEMBERS
Have a fun with this ppt submit ur project ….. With no tension …
If u r satisfied then contact my facebook account . Search “Rishabh Kanth” on facebook and at Gmail “[email protected]” .
Thanking u 4 looking . May this Ppt helps you.
