What are Number Systems and Number Base?

The processors process and store the data according to the principles of a different number system of number systems that we use in daily life. That's why it is necessary to know the binary number system in order to understand the structure of the processors and the software. In addition, the Octal Num System and Hexadecimal Number systems, which are close to the binary number system, will be useful for learning

number systems

What is a Number Base?

The numbers used in the counting are the ways in which they are shown in writing. The usual method of counting and writing since ancient times is the technique of counting tens (it is suggested that it was born from counting with ten fingers). Numbers are expressed using 10 digits in the deluded counting and writing technique. Numbers written in this way (i.e. a total of 10 digits, 0123456789 digits) are called 10-based numbers.

How Many Different Number Bases Are There?

There are as many number bases and number systems as you can express each number with another character. But too much grassroots diversity does us no good. Considering that all 26 letters and 10 digits in the English alafabe in general are used, we can do base arithmetic up to 36 bases (no 1-based, 35 separate bases in total). If we wish, we can accept small and uppercase letters as separate numbers and increase the base number.

Number Bases Used on Computers

Some number bases are preferred on computers because they are easy and fast to translate on a computer. For example, a binary system consisting of 2 digits (0 and 1 digits) and a 16-digit system consisting of 16 digits. The binary number system also forms the basis of the computer's operating logic. In computer recording units, it records the data in the binary system and processes the data on the binary equivalent of the data in memory. Microprocessors (CPUs) also process data on a binary system.

Cases where the Number of Digits Is More Than 10

When the number of numbers is more than 10, letters in the English alphabet are used as numbers. For example, the numbers of the 16-digit system consisting of 16 digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F respectively (A is a number whose number value is 10 in the ten system and F is 15 in the de ten system).

How to Convert a Number at Base 10 to Another Base

The number is divided as much as the base can be divided by the number of digits. When the remains of the section are written from end to end, the number is 10 equivalent.

Example: The baseline equivalent of 35 is as follows:

35 / 2 = 17, Remaining = 1

17 of 2 = 8, Remaining = 1

8 / 2 = 4, Remaining = 0

4 / 2 = 2, Remaining = 0

2 of 2 = 1, Remaining = 0

1 / 2 = 0, Remaining = 1

When numbers are typed from end to end, the value 100011 is found. That is, 35 = (100011)2.

Example 2: The baseline equivalent of 1250 is:

1250 / 16 = 78, Remaining = 2

78 / 16 = 4, Remain = 14

4 of 16 = 0, Remain = 4

 

When the numbers are written with the corresponding numbers in the 16-way system from end to end, there is 4E2 (E is the number 14). That is, 1250 = (4E2)16.

Two-Based Number System / Binary

There are two numbers in the binary number system, which are 0 and 1. Therefore, the base of the binary number system is 2.(1011 )2. This number system is called binary numbers, which means binary number in English. Each number is expressed as dijite and the digits are written as the force of 2. For example, a 4-bit number consisting of 4 digits (1011 )2 has bit weights of 2³,2²,2¹.2º. The dijite with the smallest bit weights is called the smallest significant digit (LSD) and the digit with the largest bit weight is called the most significant digit. The MSB side is the most weighted bit, the LSB side is the smallest valued bit. In electrical logic, there is 1 electric (current va or voltage), 0 means no electricity (current va or voltage).

Eight-Based Number System / Octal

There are 8 digits in the octal number system. These are 0 1 2 3 4 5 6 7. The base number is 8. (125)8.

Decimal Number System / Decimal

The decimal number system consists of normal counting numbers. That is, it consists of the numbers 0 1 2 3 4 5 6 7 8 9. It is the number system that we use in our daily lives. Since there are ten numbers, the base of this number system is 10. (348)10. In this number system, four mathematical processes are known.

Sixteen-Based Number System / Hexadecimal

There are 16 digits in the hexadecimal number system. These are 0 1 2 3 4 5 6 7 8 9 A B C D E F. Corresponds to 10=A,11=B, 12=C, 13=D, 14=E, 15=F. The base is 16. (1B3A)16. Software installed on microprocessors is installed thanks to this number system.

Base Converter