# Number Base System - Table showing the Number Bases with explanations

### Introduction to Number Bases:

Numbering begins with 0 (zero). Also, numbers are expressed in bases (sometimes called radix). A base 10 number for instance will comprise of 10 digits ranging from 0 – 9.

Note: We generally use base 10 in our numbering system.

Base 10 digits will comprise of: 0 1 2 3 4 5 6 7 8 9

Since the above numbers are composed of 10 digits, Base 10 may be referred to as decimals or denary digits.

The table below illustrates base 10 digits:

Apart from base 10 (Decimal), we also have other bases like:

• Base 2 also called Binary: consists of 2 digits which are 0 and 1
• Base 3 also called Ternary: consists of 3 digits which are 0, 1 and 2
• Base 4 also called Quaternary: consists of 4 digits which are 0, 1, 2 and 3
• Base 5 also called Quinary: consists of 5 digits which are 0, 1, 2, 3 and 4
• Base 6 also called Senary: consists of 6 digits which are 0, 1, 2, 3, 4, 5 and 6
• Base 7 also called Septenary: consists of 7 digits which are 0, 1, 2, 3, 4, 5, 6 and 7
• Base 8 also called Octal: consists of 8 digits which are 0, 1, 2, 3, 4, 5, 6, 7 and 8
• Base 9 also called Nonary: consists of 9 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

Note: When we have a base number greater than 10; for instance base 11 or base 12 or base 13 and so on, the next digit will be an alphabet in its ascending order.

Let's see the examples below:

• Base 11 also called Undecimal: consists of 11 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A
• Base 12 also called Duodecimal: consists of 12 digits which are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B

Note: Base 16 is also known as hexadecimal digits.

The digits for base 16 (Hexadecimal digits) are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

With regards to base 2, it will comprise of only 2 digits which are 0 and 1.

Since we have just 2 digits here, base 2 is often referred to a binary digit.

Binary digits are fundamental to how computers work. This is why you may see stuffs like "01001100101011011" in a programming or computer language. Remember, we have just two digits in binary and that’s 0 and 1.

The table below shows what base 2 would look like:

 Base 1 Base 2 Summary 0 All base digits starts at 0 1 1 Next digit is 1. Base 2 digit ends with 1 11 10 We start at zero again, but add 1 to the left 111 11 We will add 1 digit to the right 1111 100 Since the above digits is all 1’s and base 2 ends with digit 1, we will change all the 1’s to 0’s and add 1 to the left 11111 101 We will add one to the farthest 0 at the right

Note: Understanding base 2 is very vital for Internet Protocol address (IP Address) in computer networking.

Ternary or Base 3 comprise of 3 digits which are 0, 1 and 2.

The table below shows what base 3 would look like:

 Unary/Base 1 Base 3 Summary 0 All base digits starts at 0 1 1 Next digit is 1. 11 2 Next digit is 2. Base 3 digit ends with 2 111 10 We will start back at 0 and add 1 to the left 1111 11 Next digit is 1 from the right 11111 12 Next digit is 2 from the right 111111 20 We will start back at zero and add one to the left 1111111 21 We will add 1 to the right 11111111 22 We will add 1 to the right 111111111 100 Since the above digits is all 2’s, we will change all  the 2’s to 0’s and add 1 to the left 1111111111 101 We will add 1 to the farthest right

The table below shows a summary of base 10, base 2, base 6, base 11 and base 16 respectively.

 Unary Base 10 Base 2 Base 6 Base 11 Base 16 1 1 1 1 1 1 11 2 10 2 2 2 111 3 11 3 3 3 1111 4 100 4 4 4 11111 5 101 5 5 5 111111 6 110 10 6 6 1111111 7 111 11 7 7 11111111 8 1000 12 8 8 111111111 9 1001 13 9 9 1111111111 10 1010 14 A A 11111111111 11 1011 15 10 B 111111111111 12 1100 20 11 C 1111111111111 13 1101 21 12 D 11111111111111 14 1110 22 13 E 111111111111111 15 1111 23 14 F 1111111111111111 16 10000 24 15 10

Notice that we skipped the zero (0) value in the above table.

Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.

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