Binary Tutorial (Part 1: Converting Binary to Base 10)
You probably clicked this because you want to learn binary. First, I’ll explain what binary is. Binary is a numeral system that uses 1s and 0s to express values, much like the customary numeral system that uses digits 0-9. The more correct term for binary is “base 2,” while the more correct term for the customary numeral system is “base 10.” You should remember these terms because I’m going to use them a lot in the tutorial.
In base 10, you have 10 numbers to represent values, 0-9. How you find the value that is represented by the numbers is shown in an example below.
1 2 3
100 10 1
The example number shown above is 123. How we find the value is by multiplying the place by the corresponding digit and add the results together, to get 123 (100 + 20 + 3 = 123). Here is another example below.
5 7 3 7 2
10000 1000 100 10 1
The number that we used was 57372. To find the value of the number, once again, you would multiple the places by the corresponding digits, and add the results together, which would result in a final answer of 57372, the number we are trying to represent (50000 + 7000 + 300 + 70 + 2).
In base 2, you only have two numbers to represent values, 1, and 0. A random example of a base 2 value is 10100, which is 20 in base 10. In base 2, the places that you would normally find in base 10 (ex. 1s, 10s, 100s...) start with 2 and double as you go on. Here is an example of the first few base 2 places: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... Below is an example of converting a base 2 value into base 10.
1 0 0 1 0 1
64 32 16 8 4 2
The base 2 value above, 100101, in base 10, is 74. You can find this by using the same method we used with base 10. You multiply the binary value by its place and add all of the results together. This should result in 74 (64 + 8 + 2). This method can be used to convert any base 2 value into base 10. You just need to keep doubling the place as the number gets longer (1, 2, 4, 8, 16, 32, 64, 128, 256, 512...) One thing to note is the the smallest value does not start with 0, it starts with 2. Just think of it like doubling 0 wouldn’t get you anywhere, so it starts at 1. (Once again, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512...) A simpler example is provided below.
1 0 1
8 4 2
The number you should have calculated is 10. Below are some random base 2 values that you can practice turning into base 10. You will probably need a sheet of paper. The answers can be found at the end of the exercise.
1. 1 0 0 0 1
2. 1 0 1 0 0 1
3. 1 0 0
4. 0 1 1
Answers and Explanations:
1. For number 1, you should have a result of 17. How this answer is found is by adding 16 + 1 to get a final answer of 17.
2. For number 2, you should have a result of 41. How this answer is found is by adding 32 + 8 + 1 to get a final answer of 41.
3. For number 3, you should have a result of 4. How this answer is found is by multiplying the 1 by the 4s place, and resulting in 4. There is no addition as all of the other numbers are 0s.
4. Number 4 was sort of a trick question. You should have resulted with 3. The 0 at the beginning is unnecessary as it does not multiply by its place to anything.
Base 10 to Binary Tutorial is coming soon! Make sure you share this with friends so they can learn too!
I did write this tutorial myself, so it would be extremely helpful if you donated! Addresses can be found below. Thanks for reading!
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