## How to Easily Change Hexadecimal or Binary into Decimal Numbers     This is an easy video on converting binary or hexadecimal into decimal numbers. This shows how to do it the easy way with windows calculator, and how to easily do it by hand.

It may be hard to wrap your head around the concept of hexadecimal and binary. Why do we need them? How do we use them? The simplest explanation I’ve found to use for people, is think about our normal number system. It goes from 0-9, which is 10 numbers. We have ten fingers and ten toes, so it’s pretty reasonable to think about how the system came about. Hexidecimal is extremely like the decimal number system, but instead of going 0-9, it goes 0-15. So just imagine that we had more numbers after 9 before we rolled over to using a one in the next column, and that’s how hexadecimal works. After you get to 9, then you use other symbols to represent the numbers through 15, and those symbols are A-F. We could have thought up new symbols to use that look like the current numbering system, but it was just easiar to pick symbols we were already familiar with.

Decimal is the opposite in a way. Instead of counting 0-9, we just count 0-1. This may seem impractical, because it takes a lot of digits to make a big number compared to decimal, but it is INCREDIBLY useful, because of how computers work. In general, a transistor has two states, on and off. This lends itself to binary very easily, so binary is really used as the computer language, because there are only two values, 0 and 1. After we count to one, then we roll over to a one in the next column.

We use hexadecimal because it works much better with binary then decimal does. This is basically because 16 is a multiple of 2, while ten is not. As in, it is much easiar to make binary into hexadecimal and back then it is decimal, so when it comes to computers, decimal is pretty useless. Basically, when it comes to computers, Binary is used for small numbers, and hexadecimal is used for large numbers. You may also see octal used (0-8) and this is because it is also easier to convert from binary than decimal because it is a multiple of 2.

These are the basic reasons why hexadecimal and binary actually exist. But we humans use decimal, so how do we go about making the stuff that’s readable to computers, or readable to humans?

To convert binary or hexadecimal into a decimal number, there are a couple simple ways. First, you can use a calculator, such as the built in Windows Calculator to convert binary or hexadecimal into decimal and back. This is very simple process and is shown in the video. The second version is by hand, which is also shown in the video. I will explain both in the steps, so if you want the how to on the calculator, skip to the step where that starts.

Each version has a subheading, so scroll to where the one you want is.

How to convert Binary into Decimal

Step 1: Converting binary to decimal is as simple as making a table that shows each of the values of a digit, and if there is a one there, add it to the total, and if there is a 0, skip it. The chart I mean is shown below, for the binary number 1101:

 8 4 2 1 1 1 0 1

This means that to get the Decimal equivalent of binary 1101, we add 8+4+1 to get 13. This is because there is a one under those three numbers in the table. The top numbers come from what each column is worth. This is very similar to the decimal system with it’s 1’s place, 10’s place, 100’s place and so on. With binary instead of a having a ones place, then a tens place, you have a 1’s place, then 2’s place, then 4’s place, then 8’s place, then 16’s, and it keeps going like that. Each column is the next multiple of 2 (2^0 = 1, 2^1 = 2, 2^3 = 8, 2^4 = 16 and so on). So a chart for decimalfor the number 1234 would look like this:

 1000 100 10 1 1 2 3 4

So we would add together 1000+200+30+4, which is equal to 1234. So the binary system is exactly like the decimal system, it just uses a different base (base 2 instead of base 10).

So if we wanted to convert a longer binary number into decimal, such as 10101100, we can use the same chart, we just have to make it bigger.

 128 64 32 16 8 4 2 1 1 0 1 0 1 1 0 0

Now since there are 1’s in the columns that are 128, 32, 8, and 4, we just add those numbers together to get the decimal equivalent of 10101100. So 128+32+8+4 = 172. Go ahead and check the conversion on a calculator, or at a conversion site like this online binary and hexadecimal conversion calculator. You can do binary numbers of any length this way, because binary numbers have infinite leading 0’s just like decimal numbers. As in 049 is the same as 49 in decimal, 01 is the same as 1 in binary.

How to Convert Hexadecimal to Binary and to Decimal