Binary to Decimal, Hex & Octal Conversion

Binary to Decimal, Hex & Octal Converter - step by step conversion & solved example problems to perform binaty decimal, binary to hexadecimal & binary to octal conversion. The binary number system is the most influential & popular number system in the context of digital computations, electronics engineering & tele communications etc. It's also called base-2 number system only uses 0 and 1 to represent any sort of information. Generally 0 represents LOW or OFF state and 1 represents HIGH or ON state. In the context of digital computations, it's frequently required to convert binary numbers into other popular representations like in decimal, hexadecimal & octal number systems, where this Binary to Decimal, Hex & Octal Converter can be employed to perform such conversions easily. Besides, the step by step calculation along with solved example problem let the users easily understand how manually perform such conversions.

Binary to Decimal Conversion

The binary number system is not the usual number system to easily understand & to read for humans, therefore, it is often required to convert the binary number into its equivalent decimal number to make it easily readable. The below step by step conversion & solved example let the users to understand how to convert binary to decimal number. The rightmost digit of the binary number has the weightage of 2⁰ and the power of 2 will increase by 1 for each successive digit from right to left (see the solved example below). It's also called as the place value of binary digits. The sum of products of binary digits & place value provides its equivalent decimal value.

Step by step conversion:
step 1: Multiply the binary digit with place value for each digit. For example, for the binary number 1010, it would be like 0 x 2⁰ = 0, 1 x 2¹ = 1, 0 x 2²
= 0 & 1 x 2³ = 8.
step 2: Sum all the product values provides an equivalent decimal.

Solved Example:
Convert the binary 100101 to its decimal equivalent


[(1) x 2⁵] + [(0) x 2⁴] + [(0) x 2³] + [(1) x 2²] + [(0) x 2¹] + [(1) x 2⁰]
[1 x 32] + [0 x 16] + [0 x 8] + [1 x 4] + [0 x 2] + [1 x 1] = 37
The decimal equivalent for binary 100101 is 37.

Binary Fraction to Decimal Conversion
Solved Example:
The below solved example let the users to know how to convert fractional binary number 10101.0101 to its equivalent decimal form
[1 x 2⁴] + [0 x 2³] + [1 x 2²] + [0 x 2¹] + [1 x 2⁰] . 0 x 2^-1 + 1 x 2^-2 + 0 x 2^-3 + 1 x 2^-4
(16 + 0 + 4 + 0 + 1) . (0 + 0.25 + 0 + 0.0625)
10101.0101₂ = 21.3125

Binary to Hex Conversion

Binary to Hex conversion can be done by divide the bits into groups from right to left side, each containing 4 bits. If the group is lack of 4 bits then add 0 or 0s to the left hand side to make sure each group containing 4 bits. The extra bits of 0 at the left side are called padding. The below solved example let the users to understand how to convert binary to decimal number.

Step by step conversion:
step 1: Split the given binary number into groups from right, each containing 4 bits.
step 2: Add 0 or 0s to the left side if any group is lack of 4 bits.
step 3: Find the Hex equivalent for each group.
step 4: Form the each group Hex number together in the same order.

Solved Example:
Convert the binary 1011010 to Hex number


1010010₂ => 0101 1010 grouped with padding
=> 5 A
= 5A₁₆

Binary to Octal Conversion

Binary to Octal conversion can be done by divide the bits into groups from right to left side, each containing 3 bits. If the group is lack of 3 bits then add 0 or 0s to the left hand side to make sure each group containing 3 bits. The extra bits of 0 at the left side are called padding. The below solved example let the users to understand how to convert binary to octal number.

Step by step conversion:
step 1: Split the given binary number into groups from right, each containing 3 bits.
step 2: Add 0 or 0s to the left side if any group is lack of 3 bits.
step 3: Find the Octal equivalent for each group.
step 4: Form the each group Octal number together in the same order.

Solved Example:
Convert the binary 10110 to Octal number


10110₂ => 010 110 grouped with padding
=> 2 6
10110₂ = 26₈
In number conversion, is being used in various general & digital applications, therefore, sometimes it's important to convert binary numbers into various representations & number systems. Here, the above step by step calculation & solved examples may useful for users to understand how the values are being used in binary conversions, however, when it comes to online for quick calculations, this binary to decimal, hex & octal converter helps the user to perform & verify such calculations as quick & easy as possible.