Computing INT_MAX and INT_MIN with Bitwise operations

Prerequisites :
INT_MAX and INT_MIN in C/C++ and Applications.
Arithmetic shift vs Logical shift

Suppose you have a 32-bit system :
The INT_MAX would be 01111111111111111111111111111111 and INT_MIN would be 10000000000000000000000000000000. 0 & 1 in most-significant bit position representing the sign bit respectively.

Computing INT_MAX and INT_MIN In C/C++ :
The number 0 is represented as 000…000(32 times).

  • We compute the NOT of 0 to get a number with 32 1s. This number is not equal to INT_MAX because the sign bit is 1, i.e. negative number.
  • Now, a right shift of this number will produce 011…111 which is INT_MAX.
  • INT_MIN is NOT of INT_MAX.

Note :
0 should be taken as unsigned int.

Reason :
If 0 is signed, during Step 2, right shift of 111..111 will yield 111…111. This is because arithmetic right shift preserves the sign of the number.
In Java, we have the feature of logical right shift available to us.

C/C++


[sourcecode language=”CPP” highlight=””]
// CPP code to compute INT_MAX and INT_MIN using
// bitwise operations
#include <bits/stdc++.h>
using namespace std;

void printMinMaxValues()
{
// 0 saved as unsigned int
unsigned int max = 0;

// Computing NOT of 0
max = ~max;

// 1 time arithmetic right shift
max = max >> 1;

// Computing INT_MIN
int min = max;

// INT_MIN = ~INT_MAX
min = ~min;

// Printing the result
cout << "INT_MAX : " << max
<< " INT_MIN : " << min;
}

// Driver code
int main()
{
printMinMaxValues();
return 0;
}
[/sourcecode]

Java


[sourcecode language=”Java” highlight=””]
// Java code to compute INT_MAX and INT_MIN using
// bitwise operations
public class Solution
{
static void printMinMaxValues()
{
int max = 0;

// Computing NOT of 0
max = ~max;

// 1 time logical right shift for INT_MAX
max = max >>> 1;

// Computing INT_MIN
int min = max;

// INT_MIN = ~INT_MAX
min = ~max;

// Printing the result
System.out.println("INT_MAX " + max +
" INT_MIN " + min);
}

public static void main(String[] args)
{
printMinMaxValues();
}
}
[/sourcecode]


Output:

INT_MAX 2147483647 INT_MIN -2147483648

Asked in : Google

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