Base numbers:
Convert other bases to base 10.
Example #1:
1 | 0 |02
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.
Convert other bases to base 10.
Example #1:
1 | 0 |02
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
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 11011112to 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 12-1012-1112and it's 157 in base 2's term.
#2: Try convert 111100112to 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 a number from base 10 to any other base
Here is a link to help you practice more of bases conversion.
Convert a number from base 10 to any other base
Here is a link to help you practice more of bases conversion.
Practice Problems: (answers below)
Convert other bases to base 10.
#: 101112
#2: 3304
#3: 1005
#4: 2103
#4: 2103
#5: 246
#6: Convert101112 to base 4
#7: Convert 1233214 to base 16 (or hexadecimal) [student Andrew's problem]
#8: 110100112 is what to base 16 ?
#9: Convert1648 to binary (or base 2) [Daniel's question]
#10: What is 100005 minus 15 ? [Remaining :Willie's questions]
#11: What is0.18to base 10?
#12: What is 5378 divided by 108 ?
#13: 3716 is what in base 4? what in base 10?