Introduction to define base in math

Base number is also known as radix. In math, some of the basic bases in number system are decimal, binary, octal and hexa-decimal. Adding the base value varies Depending on the type. For decimal the base value is 10, for octal the base value is 8, binary the base value is 2, for hexa- decimal the base value is 16. Similarly in this article we are going to discuss about the base value-10 .
Types of Base Number in Math:

Define Base ten:

Base ten is also called decimal. In math, Base ten system refers to a ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These all are non negative integers. Base ten number system is most widely used used number system.

Define Base two:

Base two is also called binary. In math, Base two system refers to a two digits 0, 1. These all are non negative integers. Base two system is highly employed in digital electronics and other machine level language circuits.

Define Base sixteen:

Base 16 is also called hexa decimal. In math, Base 16 system refers to a sixteen digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. These all are non negative integers. it is used in microprocessor and microcontroller programming.

Define Base eight:

Base 8 is also called Octal. In math, Base 8 system refers to a eight digits 0, 1, 2, 3, 4, 5, 6, 7.

Some other binary systems are base 3(Ternary or trinary ), base 4(Quaternary), base 5(Quinary), base 6(Senary), base 7(septenary), base 9(Nonary), base 11(undecimal), base 12(duo decimal) and so on upto base 36(hexatridecimal).
Example Problems for Define Base in Math:

Problem 1:

Find the decimal value of the base 8 value 1210178 using worksheet.

Solution:

Given base 8 value is 1210178

Decimal value=1*8 ^5 + 2*8 ^4+ 1*8 ^3 + 0*8 ^2 + 1*8 ^1 + 7*8 ^0

=8*8 *8*8 *8 + 2* 8*8* 8*8 + 1* 8*8* 8 + 0 + 1*8 + 7*1

= 32768 + 8192 + 512 + 0 + 8 + 7

=41487

The equivalent value in decimal is 4148710.

Problem 2:

Find the equivalent octal value from the decimal value 55510.

Solution:

Given decimal value = 55510

For converting base -8 value, we want to divide the decimal value by 8 on each step and note the remainder.

8|555
8|69 – 3
8|8 – 5
8|1 -0

From the above the octal value is obtained by noting the remainder values in orders from lower to upper.

The value is 10538

Problem 3:

Find the math equivalent hexa – decimal value from the decimal value 15309 using worksheet.

Solution:

Given decimal value =1530910

For converting base -10 value, we want to divide the decimal value by 10 on each step and note the remainder.

16|15309
16|956 – 13(D)
16|59 – 12(C)
16|3 – 11(B)

From the above the hexa – decimal value is obtained by noting the remainder values in orders from lower to upper.

The value is 3BCD16

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