what are the 3 number systems(in addition to the familiar base-10 system)are commonly used in computer science?Show how each value is represented using binary,octal,hexadecimal system?

Computers only have two numbers they can work with. These are 0 and 1. Think of it as switches: a switch can either be turned on (1) or off (0). Everything on computers are translated into a massive series of swtiches. For instance, in one method of turning letters into swtiches known as ASCII, the letter "B" (capital B) is stored as "01000010". This method of representing everyting as ones and zeroes is known as binary, or base-2.

Base-2 is called base-2 because there are two characters tht can be used to express numbers, 0 and 1. Base-10 has ten: 0-9. However, it seems uite inefficent to express numbers in base-2, because we as humans have a lot more characters at our disposal! The other two number systems, therefore, condense the base-2 system into fewer characters, but the same amount of data.

The first system is octal, or base-8. It uses the characters 0-7 to represent numbers. In this system, each base-8 character takes the place of 3 base-2 numbers. For instance, the decimal number 69 is represented in binary as 1000101. In octal, this becomes 105. Grouping into groups of three from right to left: 101 in base 8 is 5; 000 in base 8 is 0; and 1 in base 8 is 1.

Hexadecimal, base-16, quite a bit more common, is used to represent 4 base-2 characters per base-16 character. It uses the numbers 0-9, as well as the letters A-F. We can convert between them by dividing the binary number into groups of four. Again, 69 in base-10 is 1000101. "0101" in base-16 is 5, while "100" in base-16 is 4, giving the number 45. Therefore, 69 in base-10 is 45 in base-16, 105 in base-8 and 1000101 in base-2.