Hexadecimal System - Decimal to hexadecimal, hexadecimal to binary, binary to hexadecimal, octal to hexadecimal

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The hexadecimal number can be converted into other three possible number systems.

  • Hexadecimal to Binary
  • Hexadecimal to Octal
  • Hexadecimal to Decimal
let's discuss all the conversions with simple exampples.

Hexadecimal to Binary

  • Step 1:

    For each digit of hexadecimal, write the corresponding 4 bits binary code.

  • Step 2:

    Combine all the binary bits to get the final result.

	For example:
	To covert the hexadecimal number(A5.1)16 into binary number.

	1. For each digit of hexadecimal, write the corresponding 4 bits binary code.

			(A5.1)16 ====> 1010  0101 .  0001

	2. Combine all the binary bits to get the final result.

			(A5.1)16 ====> (10100101.0001)2

Hexadecimal to Octal

  • Step 1:

    For each digit of hexadecimal, write the corresponding 4 bits binary code.

  • Step 2:

    Next, group three bits on the binary number, if there will be one or two-bit, are left on the group, we need to add the required number of zeros (at the end of both sides) to make them a group.

  • Step 3:

    Finally, write the corresponding octal number for that group of three-bit binary code.

	For example:
	To covert the hexadecimal number(22.1)16 into octal number.

	1. For each digit of hexadecimal, write the corresponding 4 bits binary code.

			(22.1)16 ====>0010 0010 .  0001

	2. Combine all the binary bits to get the binary number. Then, group three bits on the binary number,

			(22.1)16 ====> (00100010.0001)2

			(22.1)16 ====> 00 100 010.000 1 (add zeros on both side)

			(22.1)16 ====> 000 100 010 . 000 100

	3. Finally, write the corresponding octal number for that group of three-bit binary code.

			(22.1)16 ====> (042.04)8 ====> (42.04)8

Hexadecimal to Decimal

  • Step 1:

    First, perform the multiplication of each hexadecimal digit with the corresponding positional value.

  • Step 2:

    Next, add all the products to get the final decimal value.

	For example:
	To covert the hexadecimal number(A5.1)16 into decimal number.

	1. Multiplay each digit of hexadecimal with coressponding positional values.

			(A5.1)16 ====> A * 161 + 5 * 160 + 1 * 16-1

	2. Add all the products to get the final decimal value.

			(A5.1)16 ====> 10 * 16 + 5 + 1 / 16

			(A5.1)16 ====> 160 + 5 + 0.0625

			(A5.1)16 ====> (165.0625)10

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Hexadecimal System - Decimal to hexadecimal, hexadecimal to binary, binary to hexadecimal, octal to hexadecimal

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The hexadecimal number can be converted into other three possible number systems.

  • Hexadecimal to Binary
  • Hexadecimal to Octal
  • Hexadecimal to Decimal
let's discuss all the conversions with simple exampples.

Hexadecimal to Binary

  • Step 1:

    For each digit of hexadecimal, write the corresponding 4 bits binary code.

  • Step 2:

    Combine all the binary bits to get the final result.

	For example:
	To covert the hexadecimal number(A5.1)16 into binary number.

	1. For each digit of hexadecimal, write the corresponding 4 bits binary code.

			(A5.1)16 ====> 1010  0101 .  0001

	2. Combine all the binary bits to get the final result.

			(A5.1)16 ====> (10100101.0001)2

Hexadecimal to Octal

  • Step 1:

    For each digit of hexadecimal, write the corresponding 4 bits binary code.

  • Step 2:

    Next, group three bits on the binary number, if there will be one or two-bit, are left on the group, we need to add the required number of zeros (at the end of both sides) to make them a group.

  • Step 3:

    Finally, write the corresponding octal number for that group of three-bit binary code.

	For example:
	To covert the hexadecimal number(22.1)16 into octal number.

	1. For each digit of hexadecimal, write the corresponding 4 bits binary code.

			(22.1)16 ====>0010 0010 .  0001

	2. Combine all the binary bits to get the binary number. Then, group three bits on the binary number,

			(22.1)16 ====> (00100010.0001)2

			(22.1)16 ====> 00 100 010.000 1 (add zeros on both side)

			(22.1)16 ====> 000 100 010 . 000 100

	3. Finally, write the corresponding octal number for that group of three-bit binary code.

			(22.1)16 ====> (042.04)8 ====> (42.04)8

Hexadecimal to Decimal

  • Step 1:

    First, perform the multiplication of each hexadecimal digit with the corresponding positional value.

  • Step 2:

    Next, add all the products to get the final decimal value.

	For example:
	To covert the hexadecimal number(A5.1)16 into decimal number.

	1. Multiplay each digit of hexadecimal with coressponding positional values.

			(A5.1)16 ====> A * 161 + 5 * 160 + 1 * 16-1

	2. Add all the products to get the final decimal value.

			(A5.1)16 ====> 10 * 16 + 5 + 1 / 16

			(A5.1)16 ====> 160 + 5 + 0.0625

			(A5.1)16 ====> (165.0625)10

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