Why does Java think that the product of all numbers from 10 to 99 is 0?
The following block of codes gives the output as 0.
public class HelloWorld{
public static void main(String []args){
int product = 1;
for (int i = 10; i <= 99; i++) {
product *= i;
}
System.out.println(product);
}
}
Please can somebody explain why this happens?
Answer
Here is what the program does at each step:
1 * 10 = 10
10 * 11 = 110
110 * 12 = 1320
1320 * 13 = 17160
17160 * 14 = 240240
240240 * 15 = 3603600
3603600 * 16 = 57657600
57657600 * 17 = 980179200
980179200 * 18 = 463356416
463356416 * 19 = 213837312
213837312 * 20 = -18221056
-18221056 * 21 = -382642176
-382642176 * 22 = 171806720
171806720 * 23 = -343412736
-343412736 * 24 = 348028928
348028928 * 25 = 110788608
110788608 * 26 = -1414463488
-1414463488 * 27 = 464191488
464191488 * 28 = 112459776
112459776 * 29 = -1033633792
-1033633792 * 30 = -944242688
-944242688 * 31 = 793247744
793247744 * 32 = -385875968
-385875968 * 33 = 150994944
150994944 * 34 = 838860800
838860800 * 35 = -704643072
-704643072 * 36 = 402653184
402653184 * 37 = 2013265920
2013265920 * 38 = -805306368
-805306368 * 39 = -1342177280
-1342177280 * 40 = -2147483648
-2147483648 * 41 = -2147483648
-2147483648 * 42 = 0
0 * 43 = 0
0 * 44 = 0
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
0 * 97 = 0
0 * 98 = 0
Notice that on some steps the multiplication results in a smaller number (980179200 * 18 = 463356416) or incorrect sign (213837312 * 20 = -18221056), indicating that there was an integer overflow. But where does the zero come from? Read on.
Keeping in mind that int data type is a 32-bit signed, two's complement integer, here is an explanation of each step:
Operation Result(1) Binary Representation(2) Result(3)
---------------- ------------ ----------------------------------------------------------------- ------------
1 * 10 10 1010 10
10 * 11 110 1101110 110
110 * 12 1320 10100101000 1320
1320 * 13 17160 100001100001000 17160
17160 * 14 240240 111010101001110000 240240
240240 * 15 3603600 1101101111110010010000 3603600
3603600 * 16 57657600 11011011111100100100000000 57657600
57657600 * 17 980179200 111010011011000101100100000000 980179200
980179200 * 18 17643225600 100 00011011100111100100001000000000 463356416
463356416 * 19 8803771904 10 00001100101111101110011000000000 213837312
213837312 * 20 4276746240 11111110111010011111100000000000 -18221056
-18221056 * 21 -382642176 11111111111111111111111111111111 11101001001100010101100000000000 -382642176
-382642176 * 22 -8418127872 11111111111111111111111111111110 00001010001111011001000000000000 171806720
171806720 * 23 3951554560 11101011100001111111000000000000 -343412736
-343412736 * 24 -8241905664 11111111111111111111111111111110 00010100101111101000000000000000 348028928
348028928 * 25 8700723200 10 00000110100110101000000000000000 110788608
110788608 * 26 2880503808 10101011101100010000000000000000 -1414463488
-1414463488 * 27 -38190514176 11111111111111111111111111110111 00011011101010110000000000000000 464191488
464191488 * 28 12997361664 11 00000110101101000000000000000000 112459776
112459776 * 29 3261333504 11000010011001000000000000000000 -1033633792
-1033633792 * 30 -31009013760 11111111111111111111111111111000 11000111101110000000000000000000 -944242688
-944242688 * 31 -29271523328 11111111111111111111111111111001 00101111010010000000000000000000 793247744
793247744 * 32 25383927808 101 11101001000000000000000000000000 -385875968
-385875968 * 33 -12733906944 11111111111111111111111111111101 00001001000000000000000000000000 150994944
150994944 * 34 5133828096 1 00110010000000000000000000000000 838860800
838860800 * 35 29360128000 110 11010110000000000000000000000000 -704643072
-704643072 * 36 -25367150592 11111111111111111111111111111010 00011000000000000000000000000000 402653184
402653184 * 37 14898167808 11 01111000000000000000000000000000 2013265920
2013265920 * 38 76504104960 10001 11010000000000000000000000000000 -805306368
-805306368 * 39 -31406948352 11111111111111111111111111111000 10110000000000000000000000000000 -1342177280
-1342177280 * 40 -53687091200 11111111111111111111111111110011 10000000000000000000000000000000 -2147483648
-2147483648 * 41 -88046829568 11111111111111111111111111101011 10000000000000000000000000000000 -2147483648
-2147483648 * 42 -90194313216 11111111111111111111111111101011 00000000000000000000000000000000 0
0 * 43 0 0 0
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
0 * 98 0 0 0
- is the correct result
- is the internal representation of the result (64 bits are used for illustration)
- is the result represented by the two's complement of the lower 32 bits
We know that multiplying a number by an even number:
- shifts the bits towards left and adds zero bits towards right
- results in an even number
So basically your program multiplies an even number with another number repeatedly which zeroes out the result bits starting from right.
PS: If the multiplications involved odd numbers only then the result will not become zero.