## Monday, May 21, 2012

### Base Numbers: Level 1

Base numbers:

Convert other bases to base 10.
Example #1:
1 | 0 |0
22|21 |20                  0*20 + 0*21 + 1*22 = 4

Thus, 1002  = 4 in base 10
The first few base 2 (or binary system) numbers that are equivalent to their base 10 (or decimal) counterpart.
base 2                       base 10
0                               0

1                               1

10                             2

11                             3

100                           4

101                           5

110                           6

111                           7

1000                         8

1001                         9

1010                        10

Example #2:
1|  2|  45
52|51|50                    4*50 + 2*51 + 1*52  = 4 + 10 + 25 = 39

Thus, 1245 = 39 in base 10

Some important points:
* All the digits in the number has to be smaller than the base. (Why?)
* Hexadecimal is base 16. In that system, you can use numbers from "0" to "9", the same as base 10.
However, numbers 10 to 15, you use letters: A for 10, B for 11, C for 12, D for 13, E for 14 and last, F      for 15.

Short cut to some base conversions:
#1: Convert 11011112 to base 8.
Since 8 = 23, you can convert base 2 to base 8 by regrouping every 3 digits.
Thus the original number will become 1578
because if you regroup the original number starting from the right, you have 12-1012-1112 and it's 157 in base 2's term.
#2: Try convert 111100112 to base 4, which is 22 so you regroup by 2.
11 (3 in base 2)-11(3 in base 2)-00 (0 in base 2)-11(3 in base 2) so the answer is 33034.

Convert other bases to base 10.
#: 101112
#23304
#31005
#42103
#5246
#6: Convert 10111 to base 4
#7: Convert 123321to base 16 (or hexadecimal) [student Andrew's problem]
#8 110100112  is what to base 16 ?
#9Convert 1648 to binary (or base 2) [Daniel's question]
#10: What is 100005  minus 15 ? [Remaining :Willie's questions]
#11: What is 0.18 to base 10?
#12: What is 5378  divided by 108 ?
#13: 3716  is what in base 4? what in base 10?
#14: What is 12314  + 22324 ?

#1: 23
#2: 60
#3: 25
#4: 21
#5: 16
#6: 23 4
#7: 6F9 16
#8: D3 16
#9: 1110100 2
#10: 1111 5
#11: 1/ 8
#12: 53.7 8
#13: 313 in base 4 and 55 in base 10
#14: 10123 4