Number System’s
A Number system is defined as a system of writing to express numbers.
Or
Number System is used to represent a particular value to the number of digits we have.
There are 4 Types of Number Systems we have
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
Radix / Base: Number of Digits you have in a Number System
Decimal Number System
Decimal comes from the Latin word Decimus, meaning tenth, from the root word decem, or 10. The decimal system, therefore, has 10 as its base /Radix and is sometimes called a base-10 system. … The decimal point, for example, refers to the period that separates the ones place from the tenths place in decimal numbers.
Range : [0,1,2,3,4,5,6,7,8,9]
Example 1 : (14)base10 , (30)base10
How we Define it 5 and 55
Example 1:
Where we know that base is 10 here
base is 10 . So it should be 10 in Multiple
55 = [10(power)0 X 5]+ [10(power)1 X 5]
55 = 5+50
Example 2:
345
300 + 40 + 5
345 = [10(power)2 X 3]+ [10(power)1 X 4]+[10(power)0 X 5]
Same for All Number Systems with respect to their base numbers
Binary Number System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression that uses only two symbols: typically “0” and “1”. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit or binary digit.
Range : [0,1]
Example : (10)base2 , (01)base2
Octal Number System
The octal numeral system, or oct for short, is the base-8 number system and uses the digits 0 to 7, that is to say, 10 represents 8 in decimal and 100 represents 64 in decimal
Range :[0,1,2,3,4,5,6,7]
Example : (45)base8 , (34)base8
Hexadecimal Number System
Range :[0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F]
Where
A = 11
B = 12
C = 13
D = 14
E = 15
F = 16
Example : (4A)base16 , (F3)base16
