# Relationship among binary octal decimal and hexadecimal number systems

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. Nested Classes And Interfaces. Binary base 2 is the natural way most digital circuits represent and manipulate numbers.

Home Certification A programmer's guide to java certification. Other Limitations Under the License. At first blush, it seems like using any number system other than human-centric decimal is complicated and unnecessary.

Solutions to Programming Exercises. Objectives for the SCPJ2 1. We can prove that replacing each octal digit by its 3-bit equivalent binary value gives the right result:. Octal base 8 was previously a popular choice for representing digital circuit numbers in a form that is more compact than binary. Liabilities Under the License.

Almost all modern digital circuits are based on two-state switches. Language Fundamentals Chapter 2. The switches are either on or off.

Decimal base 10 is the way most human beings represent numbers. Converting between Binary, Octal, and Hexadecimal The procedure for converting an octal to a binary is shown by the arrow marked a. That means four binary digits convert neatly into one hexadecimal digit. Binary base 2 is the natural way most digital circuits represent and manipulate numbers. 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.