Number Systems

When we 1st started to learn how to count, we use ten digits, 0 through 9. This way of counting is called Decimal System. However this isn’t the only way we express numbers, with computers they use Binary and Hexadecimal Systems. In this blog, we’re going to look into how these 3 systems work.

Decimal System

When we count we start at 0, then go through each digit all the way to 9. Afterwards we simply put a 1 in front, start from 0, and start the whole process again.

From here we can isolate each digit and give it a category, 9 ones, 2 tens, 3 hundreds, 1 thousand. So 1,329 would look like this. 1000 + 100 + 100 + 100 + 10 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 1329.

Binary System

Binary works in the same way as the Decimal System but uses only 2 digits, 0 and 1.

Computers convert physical signal, such as text, numbers, graphics, or sound into binary numbers. Representing data in: 1 indicates on and 0 indicates off. Every binary number contains these two digits (0 and 1).

To understand and count in Binary number is use a base number of 2, but each position has a different value. You start by placing a 1 in the first position which equals 1 in decimal. Since 1 is the highest number in binary, if you want to move to 2, you put a 1 in the second position and replace the first position with a zero.

1 = 00000001

2 = 00000010

To go to 3, you put a 1 in the first position. The reason is because to convert a binary number to a decimal number, you add the decimal value of all the positions that contain a binary 1. So, 2 + 1 = 3.

3 = 00000011

4 = 00000100

5 = 00000101

Hexadecimal System

Hexadecimal (Hex) System uses 16 digits, using the numbers from 0 through 9 and the letters A through F. Where A=10, B=11, C=12, D=13, E=14, and F=15. Similarly, counting in Hex starts at 0 and all the way through F. Then, it resets to 0 with a 1 in front.

Hex is used because it translates well to Binary and numbers takes fewer digits. For example, the number 10:

Hex: A

Binary: 1010

Instead of using 4 digits with Binary, we could just simply use only 1 digit with Hex. Since there are only 16 options (0–15) for each place holder or position, to count higher than 15, you replace the 1st digit of F with a 0 and then in the 2nd position, add a 1, leaving a hex value of 10.