A number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and consistent rules. These symbols range from 0-9 and are termed as digits. Number System comes in handy to perform mathematical computations. That said, Number Systems can be of different types. They include:
Let us look at each of these systems in some detail.
This is occasionally denoted as the Base 10 Number System, deriving its name from the utilization of ten digits ranging from 0 to 9. Given its widespread application, you may observe that the digits to the left of the decimal point signify distinct positions, including Units, Tens, Hundreds, and beyond.
The number 1254 has 4 in the unit’s place, 5 in the tens place, 2 in the hundreds place, and 1 in the thousands place. If we were to express its value, it would be:
(1×103) + (2×102) + (5×101) + (4×100)
(1×1000) + (2×100) + (5×10) + (4×1)
1000 + 200 + 50 + 4 = 1254
To sum up, here are some important points of the decimal number system:
This is known as the Binary Number System, operating on the recognition of two binary digits: 0 and 1. The base of the Binary Number System is also referred to as the radix. Consequently, in a binary number system, a number is conventionally represented as (87065) ₂.
Converting a binary number into a decimal number involves multiplying each digit of the binary number by the corresponding power of 2, either 1 or 0. Conversely, transforming a decimal number into a binary number requires continuous division of the given decimal number by 2 until the quotient becomes 1. The resulting binary number is then written from bottom to top.
The steps involved in converting a number from the binary to the decimal system are as follows:
To sum up, here are some important aspects of the Binary number system:
The octal numeral system is the base-8 number system. It uses 8 digits from 0 to 7. With fewer digits than the decimal or the hexadecimal number system, it is prone to fewer errors. A number in the octal number system is represented with the number 8 at the base.
Let us take an example where we convert an Octal Number into a decimal.
Example: (16)8 to decimal
= 1 x 81 + 6 x 80
= 8 + 6
= (14)10
Here are some salient features of the Octal Number System:
In the hexadecimal system, numbers are written or represented with base 16. The exciting thing about this system is that in the hexadecimal system, the numbers are first represented like in the decimal system, i.e., from 0 to 9. Then, the numbers are defined using the alphabet from A to F. The base of the hexadecimal number system is 16 because it has 16 alphanumeric values. Here, A is 10, B is 11, C is 12, D is 13, E is 14, and F is 15.
As we saw in several examples above, a number can be represented in any number system and converted from one to the other.
The number 349, for instance, can be written in different ways in different number systems. The decimal number 349 can thus be represented as 15D regarding the hexadecimal number system.
Besides the above number systems, there is also the Computer Numeral System. Essentially, when we type any letter or word, the computer, in turn, translates it into numbers. The computer primarily makes use of the binary number system.
How about ending the blog with some trivia on the Number System?
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