How to Convert a Binary Number Into Hexadecimal | Number System

So, hey guys today we are going to learn “How to convert a binary number into a hexadecimal number”.

Before starting this blog let’s take a recap about what are binary decimal and a hexadecimal numbers. So, let’s started…

Binary Number

Binary numbers are those number who uses only two-digit of a number system 0(Zero) and 1(One) and their base is “2”. Example is 101, 010, 1001, 01100111, etc. These types of numbers are known as Binary Numbers.

Hexadecimal Number

A Hexadecimal Number is a number that uses 16-digits of a number system. In which the range of a hexadecimal number between 0 to 9 (0,1,2,3,4,5,6,7,8,9) and A to F (A,B,C,D,E,F). A to F is equivalent to the number 10 to 16 (10, 11, 12, 13, 14, 15, and last 16). This number system is known as Hexa-Decimal Number. Example: 9, 12, 27, 2BC, 9DF, 6EA, 5AFE etc.,

To get about more details about this topic go to this link “Computer Number System”

For better understanding let start directly with the example…

Example 1: Convert a binary number (101)2 into a Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (101)2

= 1x22 + 0x21 + 1x20

= 1x4 + 0x2 + 1x1

= 4 + 0 + 1

= 5

Hence, the decimal value 
is (5)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
5 ÷ 16055

Hence, our final answer is (5)16.

Example 2: Convert the binary number (10110)2 into a Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (10110)2

= 1x24 + 0x23 + 1x22 + 1x21 
  + 0x20

= 1x16 + 0x8 + 1x4 + 1x2 
  + 0x1

= 16 + 0 + 4 + 2 + 0

= 22

Hence, the decimal value 
is (22)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
22 ÷ 16166
1÷ 16011

Now, write all the remainder from downward to the upward manner like this = 16

Hence, our final answer is (16)16.

Example 3: Convert the binary number (11101101)2 into a Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (11101101)2

= 1x27 + 1x26 + 1x25 + 0x24 
  + 1x23 + 1x22 + 0x21 + 1x20

= 1x128 + 1x64 + 1x32 
  + 0x16 + 1x8 + 1x4 
  + 0x2 + 1x1

= 128 + 64 + 32 + 0 + 8 
  + 4 + 0 + 1

= 237

Hence, the decimal value 
is (237)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
237 ÷ 161413D
14 ÷ 16014E

Now, write the hexadecimal remainder from downward to the upward manner like this = ED

Hence, our final answer is (ED)16.

Example 4: Convert the binary number (1011001111)2 into a Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (1011001111)2

= 1x29 + 0x28 + 1x27 + 1x26 
  + 0x25 + 0x24 + 1x23 
  + 1x22 +1x21 + 1x20

= 1x512 + 0x256 + 1x128 
  + 1x64 + 0x32 + 0x16 
  + 1x8 + 1x4 + 1x2 + 1x1

= 512 + 0 + 128 + 64 
  + 0 + 0 + 8 + 4 + 2 + 1

= 719

Hence, the decimal value is
 (719)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
719 ÷ 164415F
44 ÷ 16212C
2 ÷ 16022

Now, write the hexadecimal remainder from downward to the upward manner like this = 2CF

Hence, our final answer is (2CF)16.

Example 5: Convert the binary number (10000000001)2 into Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (1000000001)2

= 1x210 + 0x29 + 0x28 + 0x27 
  + 0x26 + 0x25 + 0x24 + 0x23 
  +0x22 + 0x21 + 1x20

= 1x1024 + 0x512 + 1x256 
  + 1x128 + 0x64 + 0x32 
  + 1x16 + 1x8 + 1x4 
  + 1x2 + 1x1

= 1024 + 0 + 0 + 0 + 0 
  + 0 + 0 + 0 + 0 + 1

= 1025

Hence, the decimal value 
is (1025)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
1025 ÷ 166411
64 ÷ 16400
4 ÷ 16044

Now, write the hexadecimal remainder from downward to the upward manner like this = 401

Hence, our final answer is (401)16.

Example 6: Convert the binary number (11110000)2 into a Hexadecimal number?

Sol:

Step 1: Firstly we have to convert the given number into a decimal number. Let’s convert it…

= (11110000)2

= 1x27 + 1x26 + 1x25 + 0x24 
  + 0x23 + 0x22 + 0x21 + 0x20

= 1x128 + 1x64 + 1x32 + 1x16 
  + 0x8 + 0x4 + 0x2 + 0x1

= 128 + 64 + 32 + 16 + 0 
  + 0 + 0 + 0

= 240

Hence, the decimal value 
is (240)10

Step 2: Now, we have to divide the given number by 16 until the quotients come to 0.

Decimal No.
÷ by 16
QuotientRemainderRemainder in hexadecimal
240 ÷ 161500
15 ÷ 16015F

Now, write the hexadecimal remainder from downward to the upward manner like this = F0

Hence, our final answer is (F0)16.

Also, Read these Related Articles

Spread the love

Add a Comment

Your email address will not be published.

Difference Between Bit and Byte? What is DataBase And Its Uses Types of Computer System Evolution of Computer What is Computer System ?