# Binary decimal and hexadecimal conversions So, it is not possible to simply chunk groups of binary digits to convert the raw state of a digital circuit into the human-centric format. Fundamental Information Element of Digital Circuits Almost all modern digital circuits are binary decimal and hexadecimal conversions on two-state switches. In other words, the appropriate number system can actually make things less complicated. That means three binary digits convert neatly into one octal digit. At first blush, it seems like using any number system other than human-centric decimal is complicated and unnecessary. Decimal to Octal Here is an example of using repeated division to convert decimal to octal: Append the remainder as the next most significant digit. Hexadecimal base 16 is currently the most popular choice for representing digital circuit numbers in a form that is more compact than binary. Decimal Number Conversion article continued from previous page A repeated division and remainder binary decimal and hexadecimal conversions can convert decimal to binary, octal, or hexadecimal. Furthermore, a number can be perfectly converted between the various number systems without any loss of numeric value. Divide the decimal number by the desired target radix 2, 8, or Hexadecimal is sometimes abbreviated as hex. Hexadecimal numbers are sometimes represented by preceding the value with '0x', as in 0x1B Unfortunately, decimal base 10 is not a whole power of 2. For example, decimal converted to hex is:. Now on to octal conversions There are infinite ways to represent a number. A repeated division and remainder algorithm can convert decimal binary decimal and hexadecimal conversions binary, octal, or hexadecimal. 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 is easy to instantly comprehend the values of 8 switches represented in binary as Binary is sometimes abbreviated as bin. All four number systems are equally capable of representing any number. Divide the decimal number by the desired target radix 2, 8, or Furthermore, a number can be perfectly converted between the various number systems without any loss of numeric value. Octal is sometimes abbreviated as oct. Other fun hexadecimal numbers include: