TABLE OF CONTENTS There are four systems of arithmetic which are often used in digital circuits. These systems are:
Decimal: The decimal system has a base (or radix) of 10. Therefore it uses ten different symbols to represent numbers.
Binary: The binary system has a base of 2 and so uses only two different symbols.
Octal: The octal system has a base of 8 and uses eight different symbols.
Hexadecimal. The hexadecimal system has a base of 16. It uses sixteen different symbols.
These systems use the same type of positional notation except that the decimal system uses powers of ten, the binary system uses powers of two, the octal system uses powers of eight, and the hexadecimal system uses powers of sixteen.
Decimal numbers are used to represent quantities which are outside the digital system. The binary system is extensively used by digital systems like digital computers which operate on binary information. The octal system has certain advantages in digital work because it requires less circuitry to get information into and out of a digital system. Moreover, it is easier to read, record, and print out octal numbers than binary numbers. The hexadecimal number system is particularly suited for microcomputers.
We will briefly recount some important characteristics of this more familiar system before taking up other systems. This system has a base of 10 and is a position-value system (meaning that the value of a digit depends on its position). It...
