Numeral System
There are some systems used to represent numbers depending on the purpose and need for principles like the decimal ,binary ,octal and hexadecimal systems reviewed below are some of them:
1. Decimal System
- Is characterized by its use of the nine-digit addition to zero.
- one of the most commonly used systems.
- Using the number (10) as the basis for this system.
- Use the decimal separator shall ( . )To represent a number that contains a fractional part and therefore can Excellence.
Note : each number upped to the power of zero it will equal to 1
EX1 : 123
3*100 + 2*101 + 1*102
3 + 20 + 100
=123
If the number is a fractional
EX2: 7.52
7*100 + 5*10-1 +2*10-2
7 + 0.5 + 0.02
=7.52
2. Binary System
- Is characterized by using two digits and two (0.1), hence the name came.
- Is of the old systems.
- The number 2 is used as the basis for this system.
- It increased the importance of this system after using it in the representation of the numbers and deal with them within the electronic computer.
Note: To convert from decimal system to binary system the we use the division rule.
19 2 37 2 25 2
9 2 1 18 2 1 12 2 1
4 2 1 9 2 0 6 2 0
2 2 0 4 2 1 3 2 0
1 0 2 2 0 1 1
1 1 0 1
1
(11001)2 = (25)10 , (100101)2 =(37)10 , (10011)2 =(19)10
Note : In order to convert the number from binary system to binary system we use multiply rule.
1101 = 1 * 20 + 0 * 21 +1 * 22 + 1 * 23
= 1 + 0 + 4 + 8
= 13
10010 = 0 * 20 + 1 * 21 + 0 * 22 + 0 * 23 + 1 * 24
=0 + 2 + 0 + 0+ 16
= 18
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