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. The NOT operation takes whatever value is presented, 0 or 1, and inverts it. A one becomes a zero and a zero becomes a one. Remember that the logic gates are electronic devices built specifically for this purpose. The logic rule that they follow is whatever the input is, the output is the opposite. The AND operation takes two input values. If both are 1, the logic gate generates a 1 output. Otherwise it outputs a 0. There are four combinations of input values. Three of these combinations generate a 0, and one combination generates a 1. The OR operation also takes two input values. If at least one of the input values is 1, the output value is 1. Again there are four combinations of input values. This time three combinations generate a 1 output and the fourth generates a 0 output. 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 addresses to be grouped together or controlled by other network operations. These functions will be explained in depth later in the curriculum. Web Links How Boolean Logic Works http://www.howstuffworks.com/boolean.htm
Content 1.2 Network Math 1.2.10 IP addresses and network masks The 32-bit binary addresses used on the Internet are referred to as Internet Protocol (IP) addresses. The relationship between IP addresses and network masks will be addressed in this section. 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 class. The bits left over in the 32-bit IP address identify a particular computer on the network. A computer is referred to as the host. The IP address of a computer consists of a network and a host part that represents a particular computer on a particular network. To inform a computer how the 32-bit IP address has been split, a second 32-bit 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 sequentially 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 or host on that network. Some examples of subnet masks are: 11111111000000000000000000000000 written in dotted decimal as 255.0.0.0 or 11111111111111110000000000000000 written in dotted decimal as 255.255.0.0 In the first example, the first eight bits from the left represent the network portion of the address, and the last 24 bits represent the host portion of the address. In the second example the first 16 bits represent the network portion of the address, and the last 16 bits represent the host portion of the address. Converting the IP address 10.34.23.134 to binary would result in: 00001010.00100010.00010111.10000110 Performing a Boolean AND of the IP address 10.34.23.134 and the subnet mask 255.0.0.0 produces the network address of this host: 00001010.00100010.00010111.10000110
11111111.00000000.00000000.00000000
00001010.00000000.00000000.00000000 Converting the result to dotted decimal, 10.0.0.0 is the network portion of the IP address, when using the 255.0.0.0 mask. Performing a Boolean AND of the IP address 10.34.23.134 and the subnet mask 255.255.0.0 produces the network address of this host: 00001010.00100010.00010111.10000110
11111111.11111111.00000000.00000000
00001010.00100010.00000000.00000000 Converting the result to dotted decimal, 10.34.0.0 is the network portion of the IP address, when using the 255.255.0.0 mask. This is a brief illustration of the effect that a network mask has on an IP address. The importance of masking will become much clearer as more work with IP addresses is done. For right now it is only important that the concept of the mask is understood. Web Links IP Addressing Fundamentals http://support.wrq.com/tutorials/ tutorial.html
Content Summary An understanding of the following key points should have been achieved: