© 2010 Cisco Systems, Inc. All rights reserved. 1 Network Math

2 © 2010 Cisco Systems, Inc. All rights reserved. Decimal Numbers AKA BASE 10 Numbers

3 © 2010 Cisco Systems, Inc. All rights reserved. Decimal numbers are based on 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Decimal Number Format Ten Millions Hundred thousands Ten thousandsThousandsHundredsTensOnes 10,000,0001,000,000100,00010,0001,

4 © 2010 Cisco Systems, Inc. All rights reserved. Example: 7, = 7469 Decimal Number Format ThousandsHundredsTensOnes 7469 X 1000X 100X 10X

5 © 2010 Cisco Systems, Inc. All rights reserved. Place holders for each digit are based on a power of 10 Decimal Number Format Ten Millions Hundred thousands Ten thousandsThousandsHundredsTensOnes 10,000,0001,000,000100,00010,0001,

6 © 2010 Cisco Systems, Inc. All rights reserved. Example: 7,469 TOTAL  7469 Decimal Number Format is a Base 10 Format ThousandsHundredsTensOnes 7469 X 10 3 X 10 2 X 10 1 X

7 © 2010 Cisco Systems, Inc. All rights reserved. Binary Numbers AKA Base 2 Numbers

8 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 Place holders for each digit are based on a power of 2 Binary (BASE 2) Number Format

9 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 0 = 1 Binary (BASE 2) Number Format

10 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 1 = 2 Binary (BASE 2) Number Format

11 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 2 = 4 Binary (BASE 2) Number Format

12 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 3 = 8 Binary (BASE 2) Number Format

13 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 4 = 16 Binary (BASE 2) Number Format

14 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 5 = 32 Binary (BASE 2) Number Format

15 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 6 = 64 Binary (BASE 2) Number Format

© 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 7 = 128 Binary (BASE 2) Number Format

17 © 2010 Cisco Systems, Inc. All rights reserved. Binary numbers are based on 2 digits: 0 & 1 The decimal value of each place in a binary number can be calculated by raising 2 to the appropriate power: 2 7 = 128 Binary (BASE 2) Number Format

18 © 2010 Cisco Systems, Inc. All rights reserved. 8-BIT BINARY NUMBERS What do 8-bit binary numbers look like?  They will use the digits 0 and 1  They will be 8 bits long

19 © 2010 Cisco Systems, Inc. All rights reserved. 8-BIT BINARY NUMBERS Here are some examples of 8-bit binary numbers.    

20 © 2010 Cisco Systems, Inc. All rights reserved. 8-BIT BINARY NUMBERS There are 256 combinations of 8-bit binary numbers:  Smallest:  Largest:

21 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of the smallest 8-bit binary number? Since zero is a factor when multiplying each place value, there are 8 zeros to add together: = 0 converted to Base 10 8-BIT BINARY NUMBERS x128=00x64=00x32=00x16=00x8=00x4=00x2=00x1=

22 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of the largest 8-bit binary number? Since each place value is multiplied by 1, the 8 place values are added together: =255 converted to Base 10 8-BIT BINARY NUMBERS x128=1281x64=641x32=321x16=161x8=81x4=41x2=21x1=

23 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: = 5 converted to Base 10 8-BIT BINARY NUMBERS x128=00x64=00x32=00x16=00x8=01x4=00x2=01x1=

24 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: = 170 converted to Base 10 8-BIT BINARY NUMBERS x128=1280x64=01x32=320x16=01x8=80x4=01x2=20x1=

25 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: = converted to Base 10 8-BIT BINARY NUMBERS

26 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: = converted to Base 10 8-BIT BINARY NUMBERS

27 © 2010 Cisco Systems, Inc. All rights reserved. CONVERSIONS Binary to Decimal Decimal to Binary

28 © 2010 Cisco Systems, Inc. All rights reserved. Remember the decimal values for each placeholder in an 8-bit binary number: Converting from Binary to Decimal and Converting from Decimal to Binary utilize this These conversions will be necessary numerous times! IMPORTANT TO REMEMBER!

29 © 2010 Cisco Systems, Inc. All rights reserved.

30 © 2010 Cisco Systems, Inc. All rights reserved.