Binary Number 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.
What is Bit in Binary Number?
A single binary digit is called a “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 the 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 × 1000 + 2 × 100 + 3 × 10 + 5 × 1
Given,
1000 | = 10^{3} = 10 × 10 × 10 |
100 | = 10^{2} = 10 × 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 × 1000 + 2 × 100 + 3 × 10 + 5 × 1
= 1 × 10^{3} + 2 × 10^{2} + 3 × 10^{1} + 5 × 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 10^{0}, 10^{1} 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 10^{0}, you need to add 1 to the column 10^{1}.
We place the digits in columns 2^{0}, 2^{1} and so on in base 2. To place a value that is higher than 1 in 2^{n}, you need to add 2^{(n+1)}. For instance, to add 3 to column 2^{0}, you need to add 1 to column 2^{1}.
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 × 8 + 0 × 4 + 1 × 2 + 1 + 1 × ½ + 1 × ¼ + 0 × 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 ½ 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.
Binary Number System Table
Some of the binary notations of decimal numbers are mentioned in the below list.
Decimal number | Binary value |
---|---|
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Example Question
Let us practice some of the problems for better understanding:
Question 1: What is binary number 1.1 in decimal?
Solution:
Step 1: 1 on the left-hand side is on the one’s position, so it’s 1.
Step 2: The one on the right-hand side is in halves, so it’s
1 × ½
Step 3: so, 1.1 = 1.5 in decimal.
Question 2: Write 10.11_{2} in Decimal?
Solution:
10.11 = 1 x (2)^{1} + 0 (2)^{0} + 1 (½)^{1} + 1(½)^{2}
= 2 + 0 + ½ + ½
= 2.75
So, 10.11 is 2.75 in Decimal.