Example: converting 51 from base 8 to base 10.
Step 1: base 8 to base 2
Step 2 : base 2 to base 10
first we need convert base 8 to base 2
000 -> 0
001 -> 1
010 -> 2
011 -> 3
100 -> 4
101 -> 5
110 -> 6
111 -> 7
so 5 = 101
1 = 001
so 51 = 101001
now step 2. converting base 2 to base 10
1x25 + ox24 + 1x23+ 0x22 + 0x21 + 1x20 = 41
Answer : 41
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Well, darling, to convert 19 in base 10 to base 8, you divide 19 by 8 to get 2 with a remainder of 3. Then you take that remainder and slap it in front of the 2 to get 23 in base 8. Voila! Math made fabulous.
503 base 10 = 767 base 8 503 base 8 = 323 base 10
To add two numbers in different bases, we first convert them to the same base. In this case, we convert 43 base 5 to base 10, which is 23. Then we convert 24 base 5 to base 10, which is 14. Adding 23 and 14 in base 10 gives us 37. Finally, we convert 37 back to base 5, which is 112. So, 43 base 5 plus 24 base 5 equals 112 base 5.
11012
1. You have to know the base of the original number. 2. If the base of the original number is base 10, then you don't need to convert it to decimal because the original number is already a decimal number. This means the decimal numbering system is base 10 (i.e. it has 10 base digits-->0-9) 3. If the base of the original number is different than base 10, then you will need to use a mathematical conversion method (or a computer program/calculator) to convert the original number to decimal. For example: If the original number 1011 is a base 2 (binary) number, then you would use the following conversion method to convert it from base 2 to base 10: 1 * 2^0 = 1 * 1 = 1 1 * 2^1 = 1 * 2 = 2 0 * 2^2 = 0 * 4 = 0 1 * 2^3 = 1 * 8 = 8 Now add the right most column of numbers together (e.g.: 1+2+0+8=11). 11 is the decimal (base 10) equivalent to the original base 2 number 1011. Similar methods can be used to convert from other base numbering systems to decimal (e.g. base 5 to base 10)