# Binary hexadecimal and decimal

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: For example, switches that are 'on' are represented by '1' and switches that are 'off' are represented by '0'.

It is easy to instantly comprehend the values of 8 switches represented in binary as It is also easy to build a circuit to display each switch state in binary, by having an LED lit or unlit for each binary digit. As digital circuits grew more complex, a more compact form of representing circuit information became necessary. That means three binary digits convert neatly into one octal digit. 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.

Form the each group Hex number together in the same order.