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