1. Number systems Converting numbers between binary, octal, decimal, hexadecimal (the easy way)

2. Small numbers are easy to convert But it helps to have a system for converting larger numbers to avoid errors. 5 10 -> 101 2 12 10 = C 16 1100 2 = 12 10

3. Converting from base 10 (decimal) to base 2 (binary) example number = 42 3. Write a 1 underneath if that place value is used, 0 if not. subtract to find out what is left. Read your answer from left to right The number in binary is 101010 1. Write the powers of 2 in a row starting on the RIGHT side with a 1 2. Keep doubling (*2) until you get to something greater than your number (42) DEMONSTRATE Watch 1248163264 101 0 1 0 42 -32 ---- 10 - 8 ---- 2 -2 ---- 0 This is too big

4. Converting from base 10 (decimal) to base 2 (binary) example number = 7053 the number in binary is 1101110001101 write the powers of 2 in a row until you get to something > the number DO TOGETHER Do this together 12481632641282565121024204840968192 1 7053 -4096 ------- 2957 1 -2048 ------- 909 01 - 512 ------- 397 1 -256 ------ 141 1 -128 ------- 13 0001 - 8 ----- 5 1 -4 --- 1 1 --- 0 0 Too big

5. Do this one 150 10  binary 1 2 4 8 16 32 64 128 256 The answer is: 10010110 STUDENT’S TURN 100101 10 Click to see each digit that is needed. Too big

6. To convert binary to decimal Write the powers of 2 below each digit and only add the values with a 1 above them. the number in binary is 10111001101 1 0 1 1 1 0 0 1 1 0 1 1024 512 256 128 64 32 16 8 4 2 1 Watch 1024 + 256+128+64 + 8 + 4 + 1 = 1,485 Start at the right and double each number

7. Your turn. Convert 100010011 2 to decimal 1 0 0 0 1 0 0 1 1 256 128 64 32 16 8 4 2 1 256 + 16 + 2+1 = 275 …. And now, for more about number systems.

8. Part 2 Number Systems

9. Quick review What’s 41 in binary? The answer is: 101001 6432 16 8 4 2 1 1 0 1 0 0 1

10. Quick Review: binary to decimal 1001101 2  decimal 64 + 8 + 4 + 1 =77

11. An Introduction to Hexadecimal 16 digits Use letters when you run out of single digits 0 1 2 3 4 5 6 7 8 9 A B C D E F SO… 11 10 = ? 16  B 16 15 10 = ?  F 16 16 10 = ?  10 16

12. from base 10 to base 16 ( decimal to hexadecimal ) write the powers of 16 in a row until you get to one > the number divide the number by each power of 16 and write the answer and save the remainder 65,536 4,096 256 16 1 Too high 7053/4096 = 1 R 2957 2957/256 = 11 R 141 141/16 = 8 R 13 13 ones the numbers in hex are:  1 2 3 4 5 6 7 8 9 A B C D E F (A=10…. F=15) So your number is 1 11 8 13 = 1B8D 16 example number = 7053 Watch

13. Do this one 962 10  hexadecimal 3C2 16 This is 3*256 + C(10)*16 + 2

14. from hexadecimal (base 16) back to decimal Write the number across a row. Write the powers of 16 below it. Multiply. Then add the products. 1 B 8 D =(1X4096)+ (11*256)+ (8*16)+(13*1) = 4096 + 2816 + 128 + 13 = 7053 1B8D 16 1162564096 Watch

15. Do this one A10E 16  decimal 41230

16. Octal Base 8 Uses 8 different digits 0 1 2 3 4 5 6 7

17. from base 10 to base 8 ( decimal to octal ) write the powers of 8 in a row until you get to one > the number divide the number by each power of 8 write the answer and save the remainder 32768 4096 512 64 8 1 too high 7053/4096 = 1 R 2957 2957/512 = 5 R 397 397/64 = 6 R 13 13/8 = 1 R 5 = 5 ones so your number in octal is 15615 8 example number = 7053 Watch

18. Do this one: 946 10  octal 1662 8

19. from octal (base 8) back to decimal write the number write the powers of 8 below it and multiply. then add the products. 1 5 6 1 5 4096 512 64 8 1 1*4096 = 4096 5* 512=2560 6* 64= 384 1* 8= 8 5 * 1 = 5  added together = 7053 15615 8 Watch

20. Do this one 2045 8 1061 10

21. Binary  hex  octal If you can count from 1 to 15 in binary you have it made 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111

22. Binary to hexadecimal and hex to binary 4 binary digits correspond to 1 hexadecimal digit Start grouping digits on the RIGHT side 00000 00011 00102 00113 01004 01015 01106 01117 10008 10019 1010A 1011B 1100C 1101D 1110E 1111F To convert binary 1101011110 to hex Binary  Hexadecimal 11 0101 1110 3 5 E 35E 16 Hex  Binary 28D1 10 100011010001 2 Watch Write this down the side of your paper.

23. Practice Hex  Binary  Hex Convert E58 16 to Binary  111001011000 Convert 110010110 to Hexadecimal  196

24. binary to octal and octal to binary 3 binary digits correspond to 1 octal digit 0000 0011 0102 0113 1004 1015 1106 1117 Binary to octal 10110011 263 Octal to binary 451 100 101 001 Watch

25. Practice Octal  Binary  Octal Convert 307 8 to Binary  11000111 Convert 110010110 to Octal  646

26. octal to hex and hex to octal. Convert to binary, regroup and convert to other base. Octal to binary to hex 451 8 100 101 001 129 16 Watch

27. Practice Octal  Hex Convert 307 8 to Hex  11 000 111 first in binary  11000111  1100 0111 divide into groups of 4  12 7  C7 16

28. Practice Hex  Octal Convert 2B1D 16 to Octal  10 1011 0001 1101 first in binary  10101100011101  10 101 100 011 101 divide into groups of 3  2 5 4 3 5  25435 8

29. The End