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### Computers often express numbers in what format?

Base 16 numbering is called 'Hex' or 'Hexadecimal'. Base 8 numbering is called 'Octal'. Base 2 numbering is called 'Binary'.

### What is the purpose of the hexadecimal numbering system?

Hexadecimal number system is a number sytem with a Base of 16. The 'regular' system which we use every day is base-ten (decimal), with the digits 0-9.Having a base 16 system makes it easier to represent values of computer memory, as computers deal in binary (base 2), where every value is either one or zero (on or off).With hexadecimal, the digit values range from zero to fifteen, so symbols are needed to represent ten, eleven, ... fifteen as single digits. The letters A through F were chosen, so:A represents tenB = elevenC = twelveD = thirteenE = fourteenF = fifteen

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### What does binary mean?

Binary means consisting of or relating to 2, especially any kind of system that has two of something. The 'binary system' often means the numerical system that consists only of 0 and 1, as opposed to the decimal system that uses 10 digits. But there are binary stars, two stars that orbit around each other, and the word is used in many other ways as well.

### Why are octal or hexadecimal number systems used as shortcut notations?

With computers it is often bit (binary digit) patterns that matter and with octal or hexadecimal numbers it is easy to convert them to binary as each digit is represented by an exact number of binary digits (3 for octal, 4 for hexadecimal) without any waste.Using *nix access permissions as an example, the basic permissions are split into 3 groups (Owner, Group, World), each with 3 possible permissions (Read, Write and eXecute). These are stored as a bit pattern: if set the permission is granted, if not set permission is not granted. A file with rwxr-x--x (rwx for owner, r-x for group and --x for world) is stored in binary as 111101001 which can be represented in octal easily by reading it in groups of 3 bits: 111101001 &rarr; 111 101 001 = 0751, or in hexadecimal by splitting it into groups of 4 bits: 111101001 &rarr; 1 1110 1001 = 0x1e9; but to convert it to decimal requires: 256 + 128 + 64 + 32 + 8 + 1 = 489.Similarly, going the other way: what permissions are represented by 420?420 to binary:420 &divide; 2 = 210 r 0210 &divide; 2 = 105 r 0105 &divide; 2 = 52 r 152 &divide; 2 = 26 r 026 &divide; 2 = 13 r 013 &divide; 2 = 6 r 16 &divide; 2 = 3 r 03 &divide; 2 = 1 r 11 &divide; 2 = 0 r 1&rarr; 420 = 110100100 in binary = rw-r--r--420 in octal is 0644 and in hexadecimal is 0x1a40644 to binary: 110 100 100 &rarr; 110100100 as before [much quicker and easier]0x1a4 to binary: 1 1010 0100 &rarr; 110100100 again.

### Are Memory addresses are most often displayed in the hexadecimal numbering system?

Yes. We could use decimal notation but hexadecimal is more convenient because it requires fewer digits and more closely reflects the way the machine addresses memory using its native binary notation. For instance, a 64-bit address in decimal requires 20 decimal digits (including leading zeroes) but only 16 hexadecimal digits. Moreover, the hexadecimal value can be easily translated into the actual binary value used by the machine because each hex digit maps 1:1 with every nybble of the binary value. A nybble is half-a-byte (4-bits). Since each address typically represents an 8-bit byte, the value of that byte can also be expressed using just 2 hexadecimal digits (00 to FF) whereas decimal notation would require 3 digits (000 to 255). If we used decimal notation to present the contents of a block of memory, then we wouldn't be able to fit as many columns of data on the screen at once. More importantly, when we look at the contents of memory we're generally more interested in what the computer sees, and hexadecimal notation more closely reflects what the computer sees.

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### What is the base 2 system?

It is often called Binary. There are only 2 symbols, usually "0" and "1". Digital devices often use Binary.

### Why are these octal codes used instead of decimal system?

Octal codes are often used to write the numerical value of a binary number because it is easier to convert from binary to octal, instead of binary to decimal. You can convert to octal on sight, and it simply requires grouping the binary bits into groups of three, whereas converting to decimal requires repeated division by 10102 or 1010. Actually, grouping into three bits is the same as dividing by 1002 or 810 so the process is really the same. Divide by 8 to get octal. Divide by 10 to get decimal.

### Where did kings live in medieval times?

In his castle , where he often held court or audiences.