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09.3 Subnet Masks and Binary Numbers
9/11/2016 Cisco ELearning for ICND1 v2.0 https://ondemandelearning.cisco.com/ciscosc/icnd1#/sections/9/pages/3 1/3 Subnet Masks and Binary Numbers Section 9: IP Addressing and Subnets To understand subnetting, you must have a thorough understanding of subnet masks and binary numbers. Take a look at subnet masks first. You may have noticed that every time you see an IPv4 address (192.168.4.6, for example), you see something like this: 192.168.4.6 255.255.255.0 or 192.168.4.6/24 The numbers 255.255.255.0 and 24 in these examples are two different expressions of the subnet mask. The purpose of the subnet mask is to identify which portion of an IP address is the network address and which portion is the host address. Like the IP address, the subnet mask is made up of 32 binary bits that are divided into 4 octets of 8 bits each. Each octet is an 8bit binary number. The following table shows the binary and decimal versions of an IP address and subnet mask pair: Binary and Decimal Versions of an IP Address and Subnet Mask Pair Binary Decimal IP address 11000000.10101000.00000100.00000110 192.168.4.6 Subnet mask 11111111.11111111.11111111.00000000 255.255.255.0 Any IP address bits that have corresponding subnet mask bits set to 1 represent the network address. Any address bits that have corresponding mask bits set to 0 represent the host address. In the table above, the network portion of the IP address is 11000000.10101000.00000100, or 192.168.4, and the host address is 00000110, or 6. If the IP address and subnet mask pair in the example is expressed as 192.168.4.6/24, the 24 is simply the number of bits that are set to 1 in the subnet mask. This number is called the prefix length. 9/11/2016 Cisco ELearning for ICND1 v2.0 https://ondemandelearning.cisco.com/ciscosc/icnd1#/sections/9/pages/3 2/3 Now take a closer look at binary numbers. The binary number system is a base2 number system that uses only the numeric values 0 and 1. In the binary number system, as in the decimal number system, the actual value of each digit depends on its position within the number. As shown in the table below, the value of the farright binary digit, or bit, is 1. You can easily obtain the value of each subsequent digit by doubling the previous value as you move from right to left, as shown in the table. Binary Number System Bits 1 1 1 1 1 1 1 1 2x64 2x32 2x16 2x8 2x4 2x2 2x1 Bit values 128 64 32 16 8 4 2 1 Now that you know the value of the individual digits, you can convert numbers between the binary and decimal number systems. To convert a number from binary to decimal, simply add together the values of all bits that are turned on. A bit is considered on if it has a value of 1 . The following table shows an 8bit binary number, 10010011. Bits 128, 16, 2, and 1 are turned on, so binary 10010011 equals 147 in decimal. (128+16+2+1=147) Binary to Decimal Conversion Binary number 1 0 0 1 0 0 1 1 Value of each bit 128 16 2 1 128 +16 +2 +1 = 147 To convert from decimal to binary, select the minimal amount of digits whose combined bit values add up to the decimal value. For example, to convert the decimal number 32 to binary, you should turn on only the bit with the value of 32. Similarly, in the binary version of the decimal number 8, the only bit that should be turned on is the bit with the value of 8. Decimal to Binary Conversion 9/11/2016 Cisco ELearning for ICND1 v2.0 https://ondemandelearning.cisco.com/ciscosc/icnd1#/sections/9/pages/3 3/3 Binary number 0 0 1 0 0 0 0 0 = 32 Value of each bit 128 64 32 16 8 4 2 1 However, to convert most decimal numbers to binary, you must turn on multiple bits. The following is an example; the decimal number 67 is 01000011 in binary. Decimal Number 67 as 01000011 in Binary Binary number 0 1 0 0 0 0 1 1 = 67 Value of each bit 128 64 32 16 8 4 2 1 Up Next: Implementing Subnetting: Borrowing Bits