0 = 0 1 = 1 2 = 10 3 = 11 4 = 100 5 = 101
6 = 110 7 = 111 8 = 1000 9 = 1001 10 = 1010
PART 1 • The first chess machine
Here ' s an example of how you ' d count to ten in binary using zeros and ones:
0 = 0 1 = 1 2 = 10 3 = 11 4 = 100 5 = 101
6 = 110 7 = 111 8 = 1000 9 = 1001 10 = 1010
and so on
In the normal counting scheme that we humans use, the rightmost number represents the number of ones( through nine), the next column to the left shows the number of tens( through 9 sets of ten), the next column to the left in the number of hundreds, etc. But in binary the rightmost number is the number of ones, the next column to the left is the number of twos, the next column to the left is the number of fours, the next leftmost column is the number of eights, the next would be the number of sixteens, etc.
That explains why vacuum tubes were used. If a vacuum tube is on, that ' s a“ 1”. If the tube is off, that ' s a“ 0”. Thus“ on” and“ off” correspond to“ ones” and“ zeroes” and, by extrapolation, also to“ yes” and“ no”, which also explains how computer programs operate. A program asks a computer a question; if the answer is“ yes” the program makes the computer do one thing, while if the answer is“ no” the computer must do something else. There are no“ maybes” where digital computers are concerned; everything must be answerable by a“ yes” or“ no”.( This can make writing a program a tricky process. I used to be involved in amateur robotics, a hobby in which writing a program for a computer or robot, although it might make the machine do something relatively simple, was often an exercise in mind-bending frustration.)
No matter how complex a program may be, at its core it consists of nothing more than a series of“ yes” and“ no” questions. And although computers can do really cool things, like display pictures, show movies, do spreadsheet math, and play chess, when you strip away the layers of programming they ' re just juggling a whole lot of zeroes and ones.
17 chessking. com