Math Calculators ▶ Base Calculator
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Table of Content
An online base calculator with steps lets you convert numbers from one base to another base. Not only this, but this free base number calculator will let you apply various arithmetic operations on a couple of numbers in a certain number base system.
So it’s time to move ahead and discuss how you could carry out the calculations and conversions among various number systems.
Stay Focused!
In the light of mathematical analysis:
“A special system that allows numbers to be represented in various notations is known as the number system”
Following are the types of the number system among which conversions can be carried out by using our best base calculator with steps. Let’s discuss these one by one!
Hexadecimal to octal converter
The following table can be seen to clarify your mind concept regarding the discussion being carried out.
Decimal
base 10 |
Hex
base 16 |
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 8 |
9 | 9 |
10 | A |
11 | B |
12 | C |
13 | D |
14 | E |
15 | F |
You can also perform operations on hexadecimal numerals and get detailed results by using our number base calculator. Moreover, if you want to get a detailed map view of the hexadecimal system, you may also use our free hexadecimal calculator to do so.
You may get a thorough understanding of various system values of a number by having a look at the following table:
base 2 | base 3 | base 4 | base 5 | base 6 | base 7 | base 8 | base 9 | base 10 | base 11 | base 12 | base 13 | base 14 | base 15 | base 16 | base 17 | base 18 | base 19 | base 20 | base 21 | base 22 | base 23 | base 24 | base 25 | base 26 | base 27 | base 28 | base 29 | base 30 | base 31 | base 32 | base 33 | base 34 | base 35 | base 36 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
10 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
11 | 10 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
100 | 11 | 10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
101 | 12 | 11 | 10 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
110 | 20 | 12 | 11 | 10 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
111 | 21 | 13 | 12 | 11 | 10 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
1000 | 22 | 20 | 13 | 12 | 11 | 10 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
1001 | 100 | 21 | 14 | 13 | 12 | 11 | 10 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
1010 | 101 | 22 | 20 | 14 | 13 | 12 | 11 | 10 | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A | A |
1011 | 102 | 23 | 21 | 15 | 14 | 13 | 12 | 11 | 10 | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B | B |
1100 | 110 | 30 | 22 | 20 | 15 | 14 | 13 | 12 | 11 | 10 | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C | C |
1101 | 111 | 31 | 23 | 21 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D | D |
1110 | 112 | 32 | 24 | 22 | 20 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E | E |
1111 | 120 | 33 | 30 | 23 | 21 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F |
Moreover, adding bases as mentioned in the above table can be carried out by using this free of cost base addition calculator.
Let’s move on resolving a few example problems that will let you understand the concept map in depth properly!
Example # 01:
Convert the octal number\(\left(123\right)\) to the equivalent decimal number.
Solution:
Here we have:
$$ \left(123\right)_8= \left(1×8^{2}\right)+\left(2×8^{1}\right)+\left(3×8^{0}\right) $$
$$ \left(123\right)_8= 16 + 16 + 3 $$
$$ \left(123\right)_8= \left(35\right) $$
Which is our required answer.
Example # 01:
Add the following binary numbers:
$$ \left(101\right)_{2} \hspace{0.25in} \left(101\right)_{2} $$
Solution:
Here we are having:
(If the value become equal to or greater than 6, then we need to divide to get the remainder to down and take the carry to the next column for addition)
(1 0 1)_{2}
+ (341)_{2}
(442)_{2}
Which is required output against the input provided. For keeping you away from the complexity involved, keep using this find the base calculator absolutely for free.
Now you could instantly apply various operations on numbers bearing different bases and make conversions among base systems with this convert base calculator. Let’s find out how it actually works?
Input:
If you select calculator mode:
If you select the converter mode:
Output:
The best solve for base calculator does the following calculations for you in a blink of eye:
The corresponding number in the binary system against octal 12 is 1 that you can also cross check by this base calculator.
Different types of numbers are enlisted as follows:
Ordinal numbers are those that are used to define the position of something.
Example:
If there are 2 floors of a house, then the first floor will be represented by the 1st floor and the second one will be represented by the 2nd floor.
Number systems have great importance as they allow computer systems and such architectures to be encrypted from hacking issues. And this is why we have introduced this free different base calculator so that students may find it easy to perform various calculations and tackle the complications involved among number system conversions.
From the source of Wikipedia: Numeral system, Main numeral systems, Positional systems, Generalized variable-length integers
From the source of Khan Academy: Binary numbers, Binary numbers, Converting decimal to binary, Patterns
From the source of Lumen Learning: Binary, Octal, and Hexadecimal, Number Systems