Table of Contents
Number Bases
There are a few number systems that are used in mathematics and computer science. The two most common are base 10 and base 2. In base 10, the number 26 is written as 2×10+6. This means that 26 is two 10s added together, with 6 leftover. In base 2, the number 26 is written as 11010. This means that 26 is 11010 in binary.
Base 10 is the number system that we use in everyday life. It uses the digits 0-9. In base 2, the number 26 is written as 11010. This means that 26 is 11010 in binary. The binary number system uses the digits 0 and 1. The number 26 is two 10s added together, with 6 leftover.
What is a Base Number?
A base number is a number that is used as a multiplier in a particular number system. The most common number system in use today is the base 10 number system, which uses the digits 0 through 9. In the base 10 number system, the number 10 is the base number. This means that the number 10 can be multiplied by any other number to produce a result in base 10. For example, the number 12 can be expressed as 1 × 10 + 2 × 1, or 1,200 in base 10.
Base 2 Number System
The base 2 number system is a numeral system that uses only the digits 0 and 1. It is a positional numeral system, meaning that the position of a digit determines its value. In the base 2 number system, the value of a digit is 1 multiplied by the power of 2 that corresponds to the position of the digit. For example, the value of the digit 1 in the number 1101 is 1 multiplied by 2 to the third power, or 8. The value of the digit 1 in the number 101 is 1 multiplied by 2 to the second power, or 4.
Counting in Different Bases
Base 10
One, two, three, four, five, six, seven, eight, nine, ten.
Base 2
One, two, three, four, five, six, seven, eight, nine, ten.
Base 16
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen.
Let us Understand How to do Counting in Different Base
Base 10 counting:
In base 10 counting, the number system we use everyday, the number 10 is used as a base. The number 10 can be represented by the number 1 followed by 0 zeroes. So, the number 10 can also be represented as 1,000. In this number system, every number can be represented by a combination of 1s and 0s. For example, the number 12 can be represented as 1,000 + 2,000, or 1,100 + 1,000.
Base 2 counting:
In base 2 counting, the number 2 is used as a base. The number 2 can be represented by the number 1 followed by 1 zero. So, the number 2 can also be represented as 10. In this number system, every number can be represented by a combination of 1s and 0s. For example, the number 11 can be represented as 1,000 + 1,000 + 1, or 1,001.
(Base 2) Binary Number System Has Only 2 Digits: 0 and 1
The binary number system has only 2 digits: 0 and 1. In the binary number system, every number is represented by a combination of 0s and 1s. For example, the number 12 can be represented by the combination of 1, 2, and 0:
1
+
2
=
3
In the binary number system, the number 1 is represented by the combination of 0 and 1, and the number 2 is represented by the combination of 1 and 1. The number 3 is represented by the combination of 1, 2, and 0, and the number 4 is represented by the combination of 0 and 1, and so on.
(Base 3) Ternary Number System Has 3 Digits: 0,1, and 2
The ternary number system (base 3) has three digits: 0, 1, and 2. The ternary number system is a positional numeral system with a base of 3. It uses three symbols: 0, 1, and 2. In the ternary number system, the number 123 represents 1×102 + 2×101 + 3×100, or 1+2+3=6.
(Base 4) Quaternary Number System Has 4 Digits: 0, 1, 2, and 3
0000
0001
0002
0003
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
(Base 5) Quinary Number System Has 5 Digits: 0, 1, 2, 3, and 4
6 (Base 10) Hexadecimal Number System Has 16 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F
Base 16, or hexadecimal, is a number system that has 16 digits. The digits in hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15. Hexadecimal is used in computer programming, because it is a convenient way to represent binary numbers.
(Base 6) Senary Number System Has 6 Digits: 0, 1, 2, 3, 4, and 5
The senary number system is a base-6 number system that uses the digits 0, 1, 2, 3, 4, and 5. It is a positional system, meaning that the value of a digit depends on its position within the number. In the senary number system, the number 12345 would be written as 54321.
(Base 7) Septenary Number System Has 7 Digits: 0, 1, 2, 3, 4, 5, and 6
Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7
Nonary Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8
Binary Number System Has 2 Digits: 0 and 1
(Base 8) Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7
The octal number system is a base 8 number system. This means that the number system uses 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. In the octal number system, these digits represent the following powers of 8:
0: 1
1: 8
2: 64
3: 512
4: 4096
5: 32768
6: 262144
7: 2097152
Nonary (Base 9) Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8
The number 9 is not used in the base 9 number system.
(Base 10) Decimal Number System Has 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 9, and 10
The number 123 can be represented in the decimal number system as 1, 2, 3, 10, 11, 12.
