# Binary octal decimal and hexadecimal converter

Binary is sometimes abbreviated as bin. Octal base 8 was previously a popular choice for representing digital circuit numbers in a form that is more compact than binary. Octal is sometimes abbreviated as oct. Hexadecimal base 16 is currently the most popular choice for representing digital circuit numbers in a form that is more compact than binary. Hexadecimal numbers are sometimes represented by preceding the value with '0x', as in 0x1B Hexadecimal is sometimes abbreviated as hex. All four number systems are equally capable of representing any number.

Furthermore, a number can be perfectly converted between the various number systems without any loss of numeric value. At first blush, it seems like using any number system other than human-centric decimal is complicated and unnecessary.

However, since the job of electrical and software engineers is to work with digital circuits, engineers require number systems that can best transfer information between the human world and the digital circuit world.

It turns out that the way in which a number is represented can make it easier for the engineer to perceive the meaning of the number as it applies to a digital circuit.

In other words, the appropriate number system can actually make things less complicated. Almost all modern digital circuits are based on two-state switches. The switches are either on or off.

Because the fundamental information element of digital circuits has two states, it is most naturally represented by a number system where each individual digit has two states: Besides, the step by step calculation along with solved example problem let the users easily understand how manually perform such conversions.

The rightmost digit of the binary number has the weightage of 2 0 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. Step by step conversion: Multiply the binary digit with place value for each digit. Sum all the product values provides an equivalent decimal.

The below solved example let the users to know how to convert fractional binary number 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. Split the given binary number into groups from right, each containing 4 bits.

Add 0 or 0s to the left side if any group is lack of 4 bits. Find the Hex equivalent for each group.