I am trying to learn the binary number system but I keep coming up against a barrier to my comprehension. To people who are in the know this will no doubt seem an extremely elementary error so please be kind :). The problem concerns the eighth count. I’m going to explain my reasoning up to that point alongside the counting record in the hope that my error can be pinpointed. Apologies for being long-winded. Here goes…
- First count to 1 (from 0)
- We want to continue but have run out of digits. Therefore mark the first count with a digit on the left and begin counting from 0 again. Thus: 10 (This shows that the count is accumulative and not simply a repeat of (1) and is analogous to starting the tens column in decimal place value.)
- Simply count forward in the right column, "carrying" the 1 from the previous count to indicate place value. Thus: 11.
- Repeat the procedure at (2), getting the original 1 to budge up and put a zero to the left to show place value. Thus: 100.
- Count forward, thus: 101.
- Repeat as per (2) and (4). We now have two left columns with 1s as their value and a fresh 0 in the right column, thus 110.
- Simply count forward in the right column as per (1), (3), (5), thus: 111.
Right, the next stage [(8)] is what baffles me. I know that the next number is 1001 but I don’t understand why. Surely if we are following the pattern I have outlined above (and, assuming this is correct) the next number should be 1101, i.e we start a new column as we did when faced with 1 on the right side at (2), (4) and (6). Instead it seems to be that when we max out on 1s (i.e. 111) we have to reset several columns at once. Why am I wrong? I know it will most likely have to do with 2 being the exponent for binary numbers but I can’t make the connection and all web explanations are overly complex. Any help gratefully received.