## NETWORK MATH

### Binary presentation of data:

1 Computers work with and store data using electronic switches that are either ON or OFF. Computers can only understand and use data that is in this two-state or binary format. 1 is represented by an ON state, and 0 is represented by an OFF state. The ones and zeros are used to represent the two possible states of an electronic component in a computer. They are referred to as binary digits or bits.
2 The American Standard Code for Information Interchange (ASCII) is the most commonly used code for representing alpha-numeric data in a computer. ASCII uses binary digits to represent the symbols typed on the keyboard. When computers send ON/OFF states over a network, electrical, light, or radio waves are used to represent the 1s and 0s. Notice that each character has a unique pattern of eight binary digits assigned to represent the character.
3 Sometimes binary numbers need to be conferted to Hexadecimal (hex) numbers which reduces a long string of binary digits to a few hexadecimal characters. This makes it easier to remember and to work with the numbers.

### Bits and Bytes

1 Computers are designed to use groupings of eight bits. This grouping of eight bits is referred to as a byte. In a computer, one byte represents a single addressable storage location. These storage locations represent a value or single character of data, such as an ASCII code. The total number of combinations of the eight switches being turned on and off is 256. The value range of a byte is from 0 to 255. So a byte is an importent concept to understand...

### Base 10 Number System

1 Base 10 (0-9) is the most commmon numbering system. Binary numbers can be re-represented as base 10 ordinals.

### Base 2 Number System

1 Computers recognize and process data using the binary, or Base 2, numbering system. The binary system uses only two symbols, 0, and 1, instead of the ten symbols used in the decinal numbering system. The position, or place, of each digit from right to left in a binary number represents 2, the base number, raised to a power or exponent, starting from 0. These place values are, from right to left, 20, 21, 22, 23, 24, 25, 26, and 27, or 1, 2, 4, 8, 16, 32, 64, 128 respectively.

1 Hexadecimal (hex) is used frequently when working with computers since it can be used to represent binary numberse in a more readable form. The computer performs computations in binary, but there are several instances when the binary output of a coputer is expressed in hexadecimal to make it asier to read.

### Boolean or Binary Logic

1 Boolean logic is a binary logic that allows two numbers to be compared and a choice generated based on the two numbers. These choices are the logical AND, OR, and NOT. With the exception of the NOT, Boolean operations have the same function. They accept two numbers, which are 1 or 0, and generate a result based on the logic rule.
2 The two networking operations that use Boolean logic are subnetwork and wildcard masking. The masking operations provide a way of filtering addresses. The addresses identify the devices on the network and allows the adddresses to be grouped together or controlled by other network operations. These functions will be explained in depth later in the curriculum.

1 The 32-bit binary addresses used on the Internet are referred to as Internet Protocol (IP) addresses.
2 When IP addresses are assigned to computers, some of the bits on the left side of the 32-bit IP number represent a network. The number of bits designated depends on the address classs. The bits left over in the 32-bit IP address identify a particular computer on the network. A computer is reffered to as the host. The IP address of a computer consists of network and a host part that represents a particular computer on a particular network.
3 To inform a computer how the 32-bit IP address has been split, a second 230bit number called a subnetwork mask is used. This mask is a guide that indicates how the IP address should be interpreted by identifying how many of the bits are used to identify the network of the computer. The subnetwork mask subsequentially fills in the 1s from the left side of the mask. A subnet mask will always be all 1s until the network address is identified and then be all 0s from there to the right most bit of the mask. The bits in the subnet mask that are 0 identify the computer of host on that network.
4 Converting IP addresses to network addresses uses the network mask and a boolean AND operation (0+0=0, 0+1=0, 1+0=0, 1+1=1).

### Moo.

1 To Be continued..