Not only in mathematics but in the computer system and programming also number system has a crucial role. To express and represent numbers the concept of the number system is used in arithmetics figures. the number system has differentiation in types according to the bases. The conversion of binary to decimal forms an integral part of the mathematical system.
Table of Contents
The four basic number systems are expressed as:
- The system with Base 2, called the Binary number system.
- The system with Base 8, called the Octal number system.
- The system with Base 10, called the Decimal number system
- The system with Base 16, called the Hexadecimal number system
In this article, the Binary number system and the Decimal number system are explained in detail.
What is meant by the Binary number system?
The binary number system works using the base as numeral 2. The two important symbols on which this system depends are 1(one) and 0(zero). The system is used in basic binary coding too. In a binary system, no other numbers are used except 1 and 0 which are used as the symbols and 2 which represents the base.
Characteristics of Binary system
- A two-digit number system
- Commonly said to be Base 2 number system
- The different positions of the symbols 1 and 0 represent the same value in the power of 2.
- The leftmost position of the symbol shows the highest power
What is meant by a decimal number system?
The standard system of denoting integers and non-integer numbers of the Hindu-Arabic numeral system is called the decimal number system. The way of denoting numbers with the base as 10 is known as decimal notation. this is a positional numeral system and requires a dot(point) to represent fractions of the system.
Characteristics of the decimal number system
- The numbers are formed from the first ten numerals of (0-9) arithmetic arranged in a sequence.
- The basis of the system is the Hindu Arabic number system.
- The position of the digit in the sequence is called its place value.
- Conversion of Binary number system to Decimal number system
The basic fact to understand is that the multiplication method forms the source of binary to decimal conversion. In the process, any number with any base can be converted to a decimal (Base 10 ) number. By multiplying each digit of the sequence starting from the right towards the left i.e from the Most Significant Bit to the least with a reducing power of the base.
The formula for binary to decimal conversion
The standard formula used for converting Base 2 numbers to Base 10 numbers is
= Binary digit × 2 raised to a power of the position of the digit
The basic chart to help Binary to Decimal conversion
- Binary Decimal
- 0 0
- 1 1
- 10 2
- 11 3
- 100 4
- 101 5
- 110 6
- 111 7
- 1000 8
- 1001 9
- 1010 10
- 1011 11
- 1100 12
The above table may help in the conversion by providing the information for the basic numbers. In binary to decimal conversions, it should be remembered that the weightage of the position is added only when the respective position has a symbol 1 else if the binary position shows 0 the weightage is ignored. In simple words, this conversion means plotting every binary digit value on each column to its respective decimal digit value. Every column is defined as number 2 with an exponent. The system rises by 1 from right to left. For example – The binary number 1100101 in decimal means 1001.
Understanding conversion from Decimal to Binary
One can easily convert a Base 10(decimal number) to a base 2( binary number) very easily using the remainder method. The method is simple and you just need to divide the number with two unless you are left with a zero (be careful to take into account each remainder you obtain while dividing)
Summing up, from the above-mentioned explanation it becomes clear that though the concept of the binary number system and decimal number system may sound a bit tough it is very interesting and easy. Cuemath experts provide a practical approach by giving various examples regarding the topic to make it easy and to help the student understand it better.