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00000111 I can't figure out what this represents, and why. I'm clearly a beginner.
I got the first two questions right - 00000001 = 1 and 00000011 = 3 I can't however, get this one right: 00000111
Think about decimal notation.
If we had a number 7243:
We have a 7 in the thousands place, a 2 in the hundreds place, a 4 in the tens place, and a 3 in the ones place.
This means (7 * 1000) + (2 * 100) + (4 * 10) + (3 * 1) = Seven thousand two hundred and forty three.
Binary is similar, except instead of being able to put 10 digits in each spot (0 - 9) like in decimal notation, we can only put 2 (0-1).
So instead of having a ones, tens, hundreds, thousands, ten thousands places and so on we have:
ones, twos, fours, eights, sixteens, thirty seconds, sixty fours, and one hundred and twenty eights for the eight spaces in the example.
So, having a '1' in each of the four, two, and one places means 4 + 2 + 1 which equals 7!
If we wanted eight it would be 00001000 (a '1' in the eights place), all other numbers carry over. Just like going from 9999 to 10000.