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.
1210 = C16
510 -> 1012
11002 = 1210

3. Converting from base 10 (decimal) to base 2 (binary)
DEMONSTRATE
Converting from base 10 (decimal) to base 2 (binary)
example number = 42
Write the powers of 2 in a row starting on the RIGHT side with a 1
Keep doubling (*2) until you get to something greater than your number (42) 64 32 16 8 4 2 1
This is too big 1 1 1
3. Write a 1 underneath if that place value is used, 0 if not.
subtract to find out what is left. 42
-32
---- 10 10
- 8
---- 2 2 -2
----
Watch
Read your answer from left to right
The number in binary is

4. Converting from base 10 (decimal) to base 2 (binary)
DO TOGETHER
Converting from base 10 (decimal) to base 2 (binary)
example number = 7053
write the powers of 2 in a row until you get to something > the number
8192
4096
2048
1024
512
256
128 64 32 16 8 4 2 1
Too
big 1 1 1 1 1 1 1 1
7053
-4096
2957
2957
-2048
909
909
- 512
397
397
-256
------
141
141
-128 13 13
- 8
----- 5 5 -4
--- 1 1 -1
---
Do this together
the number in binary is

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

6. To convert binary to decimal
the number in binary is
Write the powers of 2 below each digit and only add the values with a 1 above them.
Start at the right and double each number
= 1,485
Watch

7. Your turn. Convert 1000100112 to decimal =
275
…. And now, for more about number systems.

8. Part 2
Number Systems

9. Quick review What’s 41 in binary? 32 16 8 4 2 1 1 0 1 0 0 1
The answer is:

10. Quick Review: binary to decimal
=77

11. An Introduction to Hexadecimal
16 digits
Use letters when you run out of single digits
A B C D E F
SO… = ?16
B16
1510 = ?
F16
1610 = ?
1016

12. from base 10 to base 16 (decimal to hexadecimal)
example number = 7053
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,
Too high
7053/ = R 2957
2957/256 = R 141
141/16 = 8 R 13
13 ones
the numbers in hex are:
A B C D E F (A=10…. F=15)
So your number is = 1B8D16
Watch

13. Do this one
96210  hexadecimal
3C216
This is 3*256 + C(10)*16 + 2

14. from hexadecimal (base 16) back to decimal
Watch
1B8D16
Write the number across a row. Write the powers of 16 below it. Multiply. Then add the products.
B D
=(1X4096)+
(11*256)+
(8*16)+(13*1) =
= 7053
4096
256 16 1

15. Do this one
A10E16  decimal
41230

16. Octal
Base 8
Uses 8 different digits

17. from base 10 to base 8 (decimal to octal)
example number = 7053
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
too high
7053/ = R 2957
2957/ = 5 R 397
397/64 = 6 R 13
13/8 = 1 R 5
= 5 ones
so your number in octal is
Watch

18. Do this one:
94610  octal
16628

19. from octal (base 8) back to decimal
156158
write the number
write the powers of 8 below it and multiply. then add the products.
1 * = 4096
5 * 512 = 2560
6 * 64 = 384
1* 8 =
5 * 1 =
added together = 7053
Watch

20. Do this one
20458
106110

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

22. Binary to hexadecimal and hex to binary
Watch
4 binary digits correspond to 1 hexadecimal digit
Start grouping digits on the RIGHT side
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
To convert binary to hex
Binary  Hexadecimal E
35E16
Write this down the side of your paper.
Hex  Binary
28D1

23. Practice Hex  Binary  Hex
Convert E5816 to Binary
Convert to Hexadecimal
196

24. binary to octal and octal to binary
3 binary digits correspond to 1 octal digit
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7
Binary to octal
263
Octal to binary
451
101001
Watch

25. Practice Octal  Binary  Octal
Convert 3078 to Binary
Convert 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
4518
12916
Watch

27. Practice Octal  Hex Convert 3078 to Hex 11 000 111 first in binary
divide into groups of 4
C716

28. Practice Hex  Octal Convert 2B1D16 to Octal
first in binary
divide into groups of 3
254358

29. The End