Let’s play game. Think of one number from 1 to 31 then see which table below has the number you think of.
The most left hand side table is table 1 and have weight 16. Next table 2 and have weight 8. Next table 3 and have weight 2. And the last, table 4 and have weight 1. For example, if you see you number at table 1 and 3, your number equals to weight at table 1 (1) + weight at table 3 (8) which is 9. Pretty simple isn’t it!! 😀
It’s not magic and we are using binary number to make it possible. In this example, we use 4 bit binary number. Table 4 which is the least significant number correspond to the weight 1 (20), table 3 correspond to 2 (21), table 2 correspond to 8 (23), and the last is table 1 which is the most significant number correspond to the weight 16 (24). In this example, we are not using numbers which have 1 bit on the 3rd bit which correspond to 22.
For example, if your guessed number is at table 1 and 3, those tables corresponds to weight 21 and 24. It means that those number in binary have 1 at the 2nd and the 4th bit, the rest are 0. So, your guessed number will be in the binary: 10010. If we want to make it to decimal, we have to multiply each binary digit with it’s corresponding weight. The decimal number will be 1*24 + 0*23 + 0*22 + 1*21 + 0*20 = 17. So, your guessed number must be 17.
We are very lucky that we know binary number so we can put the number in 2-Dimensional table which looks very simple to play this game. If we only know decimal number, we must put one digit in decimal number to one 10-Dimensionl table which is impossible to see without help of computer. Let’s say if you want to play guessing number with 4 digit decimal number with help of decimal number, you must use four 10D tables which is super confusing.
I’m so amazed that this simple theory about binary number, with a little modification, can be applicable to make this “magic” game. Have fun!