Binary numbers and Conversion

In our days, modern computers use electricity to work and inside of the microchip electricity is turned either on or off. And so the on-s are represented by 1 and the off-s are respectively illustrated as the 0-s. These 1 and 0-s are the binaries which are also called base 2. Thus, let's understand from where those bases came from. So basically for us to understand what are the bases, we'll just start from base 10. Why? Because we can simply count from 1 up to 10 on our 10 fingers. This means the number of numbers/symbols are equal to the base number. Thus, we can come to the binary numbers, here we have 0 and 1 so this means that it's base 2. In base 10 numbers we count from 1 to 10 but in binary numbers we have a slightly different picture here. So lets start the count 0, 1, and... we don't have the two so in this case the 2 from base 10 can be displayed in base 2 form as 10(one zero). And after the 10 it's 11(one one). Why 11? Because here we have 10+1 which is equal to 11 where 10 is 2 and 1 is 1. After those examples you may ask, so how do I understand that 11 is three? Let's see. So here we need to count and assign the number of numbers, in this example we have only 2 numbers. When assigning the numbers we are starting from the right side to the left side and when counting them we always start from 0. so 1 from 11 is the 0th and the other 1 is 1st. Here we have a function 2^n x m -
where n is the assigned number, the m is the value of number and the 2 is written there because binary numbers are base 2. So here we have 1 on the right side which is the 0th member so if we put this info into the function we'll get 2^0 x 1 = 1 and then we put the 1 on the left side and we'll get 2^1 x 1 = 2 so we basically converted these numbers to base 10 and we can easily add 1 to 2 which is 3 (1+2=3) thus we know that 11 = 3. Let's take a look at a more complicated example. So there's 10101, so at first we assign the numbers from right to left and then we do the addition. That is 2^4 x 1 + 2^3 x 0 + 2^2 x 1 + 2^1 x 0 + 2^0 x 1 = 16 + 4 + 2 = 22 we could actually ignore the multiplications with 0 (because their multiplications with any number is always 0). So it turns out to be the vice versa version of the conversion so we can convert from the base 10(decimal) numbers into binary numbers. So we have a 55 which we need to divide by 2 every time till we get to the point that the remainder is less then 2. So the division will look like this 55/2=27+(1) 27/2=13+(1) 13/2=6+(1) 6/2=3+(0) 3/2=1+(1) and (1)-because its the remainder that is smaller than 2 we simply leave this remainder so lets combine all the remainders from the last remainder up to the first. It'll be 110111 so by those remainders we got the decimal number 55 as a binary number, thus 55(base 10)=110111(base 2).