Binary Number System

According to digital electronics and mathematics, a binary number is defined as a number that is expressed in the binary system or base 2 numeral system that describes numeric values by two separate symbols; typically 1 (one) and 0 (zero). The base-2 system is the positional notation with 2 as a radix. The binary system is applied internally by almost all latest computers and computer-based devices because of its direct implementation in electronic circuits using logic gates. Every digit is referred to as a bit.

Binary numbers chart with decimal values are organized in the below column. To understand binary math, you should know how number system works. Let’s start with decimal system, since it is easier to deal with.

For example, the number to be operated is 1235.  

Thousands Hundreds Tens Ones
1 2 3 5

This indicates,

         

1235 = 1 x 1000 + 2 x 100 + 3 x 10 + 5 x 1

Given,

1000 = \(10^{3}\) = 10 x 10 x 10
100 = \(10^{2}\) = 10 x 10
10 = \(10^{1}\) = 10
1 = \(10^{0}\) (any value to the exponent zero is one)

The above table can be described as,

Thousands Hundreds Tens Ones
\(10^{3}\) \(10^{2}\) \(10^{1}\) \(10^{0}\)
1 2 3 5

Hence,

  1235 = 1 x 1000 + 2 x 100    + 3 x 10     + 5 x 1

 

= \(1 \times 10^{3} + 2 \times 10^{2} + 3 \times 10^{1} + 5 \times 10^{0}\)

The decimal number system operates in base 10 wherein the digits 0-9 represent numbers. In binary system operates in base 2 and the digits 0-1 represent numbers and the base is known as radix. Put differently, the above table can also be shown in the following manner.  

Thousands Hundreds Tens Ones
Decimal \(10^{3}\) \(10^{2}\) \(10^{1}\) \(10^{0}\)
Binary \(2^{3}\) \(2^{2}\) \(2^{1}\) \(2^{0}\)<

We place the digits in columns 100, 101 and so on in base 10. When there is a need to put a value higher than 9 in the form of 10(n+1). For instance, to add 10 to column 100, you need to add 1 to the column 101.

We place the digits in columns 20, 21 and so on in base 2. To place a value that is higher than 1 in 2n, you need to add 2(n+1). For instance, to add 3 to column 20, you need to add 1 to column 21.

Binary numbers List

Some of the binary notations of decimal numbers are mentioned below.

Decimal number Binary value
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010

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Practise This Question

ILATE rule should always be applied whenever we are using integration by parts