Binary Number System

There are many types of number systems like the whole number system or real number system, etc. Amongst these Binary Number system, Decimal system, and others are also there. Let’s have a look at what are we going to learn in this article:

  1. What is a Binary Number?
  2. How does the number system work?
  3. How does a decimal number system operate?
  4. List of Binary Numbers.
  5. Example tables of Binary number system

Binary Number System Definition:

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.

Bit:

A single binary digit is called as “Bit”. The number below has 6 bits.

110110

Binary numbers chart with decimal values is organized in the below column. To understand binary math, you should know how the 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 = 103 = 10 x 10 x 10
100 = 102 = 10 x 10
10 = 101 = 10
1 = 100 (any value to the exponent zero is one)

The above table can be described as,

Thousands Hundreds Tens Ones
103 102 101 100
1 2 3 5

Hence,

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

= 1×103+2×102+3×101+5×100

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 103 102 101 100
Binary 23 22 21 20<

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.

Position in Binary Number System

In the Binary system, we have ones, twos, fours etc…

For example 1011.110

It is shown like this:

1\(\times\)8+0\(\times\)4+1\(\times\)2+1+1\(\times\)\(\frac{1}{2}\)+1\(\times\)\(\frac{1}{4}\)+0\(\times\)\(\frac{1}{8}\) = 11.75 in

Decimal

To show the values greater than or less than one, the numbers can be placed to the left or right of the point.

10.1

10 is a whole number on the left side of the decimal and as we move more left, the number place gets bigger (Twice).

The first digit on the right is always Halves(\(\frac{1}{2}\) and as we move more right, the number gets smaller. ( half as big).

In the example given above:

  • “10” shows ‘2’ in decimal.
  • “.1” shows ‘half’.
  • So, “10.1” in binary is 2.5 in decimal.

Your turn to practice:

Question: What is binary number 1.1 in decimal?

Solution:

Step 1: 1 on left-hand side is on the ones position, so it’s 1.

Step 2: The one on the right-hand side is in halves, so it’s

1\(\times\)\(\frac{1}{2}\)

Step 3: so, 1.1 = 1.5 in decimal.

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

Which of the following is/are concave quadrilaterals?