Detect If Two Integers Have Opposite Signs

Introduction

In this question, input two numbers and detect if they have opposite signs.

Problem statement

We need to write a program to detect if two input integers have opposite signs.

Input: a = 100, b = -1
 
Output: "Signs are opposite"

Input: a = 100, b = 501
 
Output: "Signs are not opposite."

Concept

We have already learned about representing/finding a positive/negative number in the NOT lesson.

Two rules:

If the leading bit on the left side is 0, then it is a positive number.

If the leading bit on the left side is 1, then it is a negative number.

Solution

The XOR rule says the output will be 1 only when two input values are opposite (0 and 1, or 1 and 0).

The above concept clearly says if the leading left-MSB (left-most significant bit) is 1, then it’s negative.

The following four examples will clearly explain these concepts.

• Consider two numbers whose left MSBs are both 1, and the XOR of them is 0.

• If two numbers both have left MSBs of 0, then the XOR of them is 0.

• Now, when the left MSB of two inputs is different, then the XOR yields to 1, which is a negative number.

So, when we perform (x ^ y) < 0, we get the right answer.