Question
How can I read binary numbers?
Answer
Binary isn’t how we’re used to reading numbers, so no worries if it doesn’t make sense at first. Like anything, it’ll become more familiar with practice!
First, let’s break down how the base 10 number system works. This is what we use on a daily basis. The number 134 can also be looked at as 1 * 10^2 + 3 * 10^1 + 4 * 10^0, or 100 + 30 + 4.
Starting at 0 for the rightmost index, each index is the exponent of the base, and you multiply that by the number in that index. That’s why we did 4 * 10^0, because 4 is in the 0th index.
We do the same for any base, including binary.
If we have a bit string of 0b1010, we now know what to do to get the decimal number. It’s equivalent to 0 * 2^0 + 1 * 2^1 + 0 * 2^2 + 1 * 2^3, or 8 + 2, which is 10!
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Am I right in summarizing binary counting as: what is the next number, in base 10 terms, that only contains 0s and 1s?
That’s how the pattern seems to play out for me.
I also don’t understand this part of the explanation provided in this part:
‘The numbers one and zero are the same in base 10 and base 2. But in base 2, once you get to the number 2 you have to carry over the one, resulting in the representation “10”. Adding one again results in “11” (3) and adding one again results in “100” (4).’
I don’t quite get the ‘carry over the one part’
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Basically, the 2nd line means that for example, if you have 19, the next number isn’t 10 10, it’s 20, because you make the 9 a 1 and add it to the 1 (10). So in this case, you do 0 -> 1 -> 10, because that 2 is now the “ten” for power two. Then, add one to make it 11. But, what I don’t get is how 11 goes to 100. what is after 100? 101 -> 1,000 -> 1,001 -> 10,001?
There are 10 kinds of people: those who understand binary and those who do not.
Sorry. 
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Once you reach 100, you just add ones as you would in base 10 counting, but jump to the next decimal when reaching 2 in stead of 9 (for base 10 counting).
100, 101, 110, 111, 1000, 1001, 1010,1011, 1100, 1101, 1110, 1111…
Basically it means, that in base 10 system you start filling the first place of your number with numbers from 0-9, once it gets full (you reach 9) you make it 0 and move to next place and add 1 and "carry"it to the added place start counting up from 1 again, then 2 then 3…and so on (0, 1, 2…9>>> 10, 11, 12…19 >>> 20, 21, 22…29 >>> 30, 31…and so on.
in Binary system, you do the same but you only have 0 and 1 to use instead of 0-9, so you start you number with first place 0, then 1, then it gets full and you can only fill it with an extra 1 or 0, so when 1 is full you have to add a 0 to go to the next number, so its 10, then add 1, becomes 11, now 11 is full so you need to add another place so you add 0, become 100, then 101, 110, 111 is full so you add 4th place so it becomes 1000, 10001, 10010 and so on…
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thanks it was really helpful
Thank you so much! This resource saved me. 