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

#### Academic Questions in MathematicsPlease check out our Test Your Knowledge page to see all Questions and Answers Factorize 12a2 - 20a + 3 A. (6a - 1)(2a - 3) B. (6a - 1)(2a + 3) C. (6a + 1)(2a - 3) D. (6a + 1)(2a + 3) E. (-6a + 1)(2a - 3) F. (-6a + 1)(2a + 3) Simplify 10ab + 7ab A. 17ab2 B. 17a2b2 C. 3ab2 D. 3a2b2 E. 17ab F 3ab Which of the following is not a type of angle? A. Right angle B. Left Angle C. Acute Angle D. Complete Angle E. Straight Angle F. Reflex angle Two lines that can never meet each other are best considered as _____ lines. A. straight B. vertical C. horizontal D. parallel E. oblique F. perpendicular An angle at exactly 90o is a/an _____ angle. A. acute B. obtuse C. reflex D. right E. complete F. straight Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____. A. Oblique B. Curved C. Vertical D. Perpendicular E. Parallel F. Horizontal The two sides that forms an angle are referred to as the _____. A. Arms B. Vertexes C. Bays D. Zones E. Limbs F. Dune The point where the two sides of an angle meet is termed the _____. A. Arms B. Vertex C. Bays D. Zones E. Limbs F. Dune ### 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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