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

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

3. 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 10,000,0001,000,000100,00010,0001,000100101

4. 4 © 2010 Cisco Systems, Inc. All rights reserved. Example: 7,469 7000 + 400 + 60 + 9 = 7469 Decimal Number Format ThousandsHundredsTensOnes 7469 X 1000X 100X 10X 1 7000400609

5. 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 10,000,0001,000,000100,00010,0001,000100101 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0

6. 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 10 0 7000400609

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

8. 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 2727 2626 2525 2424 23232 2121 2020

9. 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 1 2727 2626 2525 2424 23232 2121 2020

10. 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 21 2727 2626 2525 2424 23232 2121 2020

11. 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 421 2727 2626 2525 2424 23232 2121 2020

12. 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 8421 2727 2626 2525 2424 23232 2121 2020

13. 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 168421 2727 2626 2525 2424 23232 2121 2020

14. 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 32168421 2727 2626 2525 2424 23232 2121 2020

15. 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 6432168421 2727 2626 2525 2424 23232 2121 2020

16. © 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 1286432168421 2727 2626 2525 2424 23232 2121 2020

17. 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 1286432168421 2727 2626 2525 2424 23232 2121 2020

18. 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. 19 © 2010 Cisco Systems, Inc. All rights reserved. 8-BIT BINARY NUMBERS Here are some examples of 8-bit binary numbers.  00000101  10101010  11001100  11100111

20. 20 © 2010 Cisco Systems, Inc. All rights reserved. 8-BIT BINARY NUMBERS There are 256 combinations of 8-bit binary numbers:  Smallest: 00000000  Largest: 11111111

21. 21 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of the smallest 8-bit binary number? 00000000 Since zero is a factor when multiplying each place value, there are 8 zeros to add together: 0+0+0+0+0+0+0+0 = 0 converted to Base 10 8-BIT BINARY NUMBERS 00000000 1286432168421 0x128=00x64=00x32=00x16=00x8=00x4=00x2=00x1=0 2727 2626 2525 2424 23232 2121 2020

22. 22 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of the largest 8-bit binary number? 11111111 Since each place value is multiplied by 1, the 8 place values are added together: 128+64+32+16+8+4+2+1=255 converted to Base 10 8-BIT BINARY NUMBERS 11111111 1286432168421 1x128=1281x64=641x32=321x16=161x8=81x4=41x2=21x1=1 2727 2626 2525 2424 23232 2121 2020

23. 23 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? 00000101 Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: 0+0+0+0+0+4+0+1 = 5 converted to Base 10 8-BIT BINARY NUMBERS 00000101 1286432168421 0x128=00x64=00x32=00x16=00x8=01x4=00x2=01x1=0 2727 2626 2525 2424 23232 2121 2020

24. 24 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? 10101010 Each zero factor will result in a zero value when multiplying the place value, but the factors of 1 will be added together: 128+0+32+0+8+0+2+0 = 170 converted to Base 10 8-BIT BINARY NUMBERS 10101010 1286432168421 1x128=1280x64=01x32=320x16=01x8=80x4=01x2=20x1=0 2727 2626 2525 2424 23232 2121 2020

25. 25 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? 11001100 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 11001100 1286432168421 2727 2626 2525 2424 23232 2121 2020

26. 26 © 2010 Cisco Systems, Inc. All rights reserved. What is the decimal value of this 8-bit binary number? 11100111 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 11100111 1286432168421 2727 2626 2525 2424 23232 2121 2020

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

28. 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! 1286432168421

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

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