**Convert Between Number Bases**

It is well known that in computer language there are four bases of numbers. The 4. numbers are binary, octal, decimal and hexadecimal. The 4. numbers are related to each other. The formula or how to find it is quite easy to learn. Conversion from decimal to non-decimal only looks for the remainder of the division. & the conversion from non-decimal to decimal is:

1. Multiply a number by its base number.

2. Each number that has a unit value is calculated to the power of ZERO (0). The tens digit, with the power of ONE (1), as well as the digits of the hundreds, thousands, and so on. The rank value always increases by one point.

**Decimal to Binary Conversion**

Conversion from decimal to binary, by division, and the result of the division is the final value.

Example: 10 (10) = …… (2)

Solution:

20 divided by 4 = 5, remainder = 0.

10 divided by 4 = 2, remainder = 1.

8 divided by 8 = 1, remainder = 0.

How to read it starting from the final result, going up, 1010.

**Binary to Octal Conversion**

The conversion method is almost the same. However, because the grouping is based on 3 bits, the result is:

1010(2) = ……(8)

Solution:

Take the last three digits first.

010(2) = 2(8)

While the remaining one last digit, still has a value of 1. The final result is: 12.

**Binary to Hexadecimal Conversion**

The conversion method is almost the same as Binary to Octal. But the grouping is 4 bits. The four rightmost bit groups are the ones position, the second four bits from the right are tens, and so on.

Example:

11100011(2) = …… (16)

Solution:

rightmost bit group: 0011 = 3

next group of bits: 1110 = E

The conversion result is: E3(16)

**Binary to Decimal Conversion**

This method or method is slightly different.

Example: 10110(2) = ……(10)

broken down into:

(1×24)+(0x23)+(1×22)+(1×21)+(0x20) = 16 + 0 + 4 + 2 + 0 = 22

The number 2 in multiplication is the binary base. While the sequential power, indicating the power of 0 is the unit, the power of 1 is the tens, and so on.

**Octal to Binary Conversion**

Actually, for this base conversion, you have to memorize the main conversion table a bit on the top page. But it can be learned easily. And take only three binaries.

Example:

523(8) = ……(2)

Solution:

By looking at the main table, the results are:

3 = 011

2 = 010

5 = 101

The ordering of numbers is still based on the positions of the units, tens and hundreds.

Result: 101010011(2)

**Hexadecimal to Binary Conversion**

The method and method is almost similar to Octal to Binary conversion. Only the grouping is four bits. As in the main table.

Example:

2A(16) = ……(2)

Solution:

A = 1010

2 = 0010

Result: 101010(2). With a note, the number “0” in the front does not need to be written.

**Decimal to Hexadecimal Conversion**

There are ways and methods, but for some people, it is still quite confusing. The simple way is, first convert from decimal to binary, then convert from binary to hexadecimal.

Example:

75(10) = ……(16)

Solution:

150 divided by 32= 4 remainder 11 (11 = B).

And the conversion result: 4B(16)

**Hexadecimal to Decimal Conversion**

The method is almost the same as converting from binary to decimal. However, the base number is 16.

Example:

4B(16) = ……(10)

Solution:

With reference to the main table, B can be written with value “11”.

(4×161)+(11×160) = 64 + 11 = 75(10)

**Decimal to Octal Conversion**

The method is almost the same as converting decimal to hexadecimal.

Example:

25(10) = ……(8)

Solution:

49 divided by 16 = 3 remainder 1.

The result can be written: 31(8)

**Octal to Decimal Conversion**

The method is almost the same as converting hexadecimal to decimal. Can be followed by the some examples below:

31(8) = ……(10)

Solution:

(3×81)+(1×80) = 24 + 1 = 25(10)