# Expert Reference Series of White Papers. Binary and IP Address Basics of Subnetting

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1 Expert Reference Series of White Papers Binary and IP Address Basics of Subnetting COURSES

3 Computers, routers, and switches use the binary numbering system. The binary numbering system is a base two numbering system, meaning there are only two base numbers zero and one. All other numbers are created from these two numbers. Just like in the decimal numbering system, the location of the number determines its value. The table below shows the value of the first eight binary positions. Base Exponent Place Value For exponents above 7, double the previous place value. For example, 2 8 = 256, 2 9 = 512, 2 10 = 1,024, and so on. Decimal to Binary Conversion Since IP addresses are a binary number represented in dotted decimal format, it is often necessary to convert a decimal number to a binary number. In the figure above, the decimal number 35 is converted to the binary number The steps to perform this conversion are below. 1. Determine your decimal number. In this scenario, it is Write out the base number and its exponent. Since an IP address uses groups of eight binary bits, eight base two exponents are listed. 3. Below the base number and its exponent, write the place value. For example, 2 0 has a value of 1; 2 2 has a value of 4; 2 3 has a value of 8; etc. 4. Compare the value of the decimal number to the value of the highest bit position. If the value of the highest bit position is greater than the decimal number, place a 0 below the bit position. A 0 below the bit position means that position is not used. However, if the value of the highest bit position is less than or equal to the decimal number, place a 1 below the bit position. A 1 below the bit position means that position is used. Copyright 2014 Global Knowledge Training LLC. All rights reserved. 3

4 In the figure, the value of the highest bit position is 128. It is greater than the decimal number 35, so a 0 is placed below the bit position of Go to the next bit position to the right. Make the same comparison and apply the same rules. In the figure, the value of the next bit position to the right is 64. It is greater than the decimal number 35, so a 0 is placed below the bit position of In the next bit position to the right, the value is 32. Thirty-two is less than 35, so a 1 is placed below the bit position of Since the bit position of 2 5 (32) is used, that means 32 of 35 have been accounted for. To determine how much is not accounted for, subtract 32 from 35. The result is 3. (35-32 = 3) 4. Compare the remaining value against the value of the remaining bit positions, moving to the right one position at a time. Since the bit positions of 2 4 (16), 2 3 (8), and 2 2 (4) are all larger than 3, a 0 is placed below each of those bit positions. 5. The bit position of 2 1 (2) is less than 3, so a 1 is placed below that bit position. This means 2 of 3 have been accounted for, so subtract 2 from 3 to determine what value is not accounted for. The result is 1. (3-2 = 1) 6. The bit position of 2 0 (1) is the same as 1, so a 1 is placed below the bit position of 2 0. This means 1 of 1 has been accounted for, so subtract 1 from 1 to determine what value is not accounted for. The result is 0. (1-1 =0) 7. This means the number is binary equivalent of the decimal number Whenever the amount remaining equals 0, then all remaining binary positions, if any, have a 0 placed below them. For example, the decimal number 160 is represented in binary by the number The table below demonstrates the process. Power Exponent Place Value Convert Decimal to Binary Calculations > Copyright 2014 Global Knowledge Training LLC. All rights reserved. 4

5 Binary to Decimal Conversion Since IP addresses are a binary number represented in dotted decimal format, it is often necessary to convert a binary number to a decimal number. In the figure above, the binary number is converted to the decimal number 185. The steps to perform this conversion are below. 1. Write out the base number and its exponent. Since an IP address uses groups of eight binary bits, eight base 2 exponents are listed. 2. Below the base number and its exponent, write the place value. For example, 2 0 has a value of 1; 2 2 has a value of 4; 2 3 has a value of 8; etc. 3. Below the place value, write the binary number. To avoid placing the wrong number in the wrong position, start at the right and move to the left. 4. Add the value of all positions that contain 1 in the binary number. In the example, the positions with values of 128, 32, 16, 8, and 1 all have binary 1s, so these values are to be added. The total is ( = = = = 185) 6. This means 185 is the decimal equivalent of Here's another example. The binary number is represented in decimal by the number 226. The table below demonstrates the process. Base Exponent Place Value Binary Number Calculations Copyright 2014 Global Knowledge Training LLC. All rights reserved. 5

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