The simplest number system is binary, which only has two digits: 0 and 1. (i.e. value of base 2). Since there are only two possible states for digital electronics (0 or 1), binary numbers are most often used by computer engineers, networking and communication experts, and other professionals today.

Hexadecimal numbers, on the other hand, have a value of 16 and only have 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. Where A, B, C, D, E, and F each represent a single bit of the decimal numbers 10, 11, 12, 13, 14, and 15.

**What is the decimal number system?**

The base 10 number system is another name for the decimal number system. It is made up of ten numbers from 0 to 9. In the decimal number system, the places to the left of the decimal point represent units, tens, hundreds, thousands, and so on. So, 10 is the starting point for the decimal number system.

**Converting binary to decimal**

Converting from a binary number system (base-2) to a decimal number system is called “binary to decimal conversion” (base-10). For computer programming, it is very important to know how to convert from binary to decimal. The binary number system only has two numbers: 0 and 1.

The decimal number system, on the other hand, has ten numbers, from 0 to 9. In the next section, we’ll learn how to change a binary number into its corresponding decimal number.

**How to Change Binary Numbers to Decimal?**

We use the multiplication method to turn the binary number into a decimal number. In this process, if a number with base n needs to be changed into a number with base 10, each digit of the given number is multiplied from the Most Significant Bit (MSB) to the Least Significant Bit (LSB) while the power of the base goes down.

**Steps to convert Binary to Decimal**

First, write down the given binary number and count from right to left the powers of 2. (powers starting from 0) Now, write each binary digit (from right to left) with the power of 2 that goes with it, so that the first binary digit (MSB) is multiplied by the biggest power of 2.

Add all the items from the step above. The answer will be the decimal number you need.

**For example:** Change the number (1101)2 from binary to decimal.

Solution:

Multiply each digit from the most significant bit to the least significant bit by 2 to the power of 2.

1 × (2)^3 + 1 × (2) ^2 + 0 × (2) ^1 + 1 × 20= 8 + 4 + 0 + 1= 13

So, the decimal number that corresponds to the binary number (1101)2 is (13).

**Converting binary to the hexadecimal system**

The hexadecimal number system makes it easy to turn large binary numbers into smaller, more compact groups. You can change a binary number into a hexadecimal number in a number of ways.

You can use either direct or indirect methods to convert. First, you have to turn a binary into a different base system (e.g., into decimal, or into octal). Then you must turn it into a hexadecimal number.

Since numbers are a type of positional number system. That means that, from right to left, the weights of the positions are 160, 161, 162, 163, etc. For the fractional part, the weights of the positions from left to right are as follows: 16-1, 16-2, 16-3, etc.

**A quick way to convert**

So, what is an easy to way to convert between number systems back and forth?

You can go online and look for a binary decimal hexadecimal converter that can convert between binary, decimal, and hexadecimal number systems instantly.

Such a calculator is able to generate results faster than the blink of an eye. So, if learning about the number systems isn’t as important to you as knowing their values, then you should use an online calculator.