How integers are stored in memory

In most modern computer systems, both positive and negative integers are stored in memory using a binary representation. This representation follows a scheme called Two's Complement for signed integers. Here's how it works:

Positive Integers:

• Positive integers are typically stored in binary format as you would expect, with a simple binary representation of the value. For example, the decimal number 7 would be stored as 0111 in binary, where the leftmost bit is the most significant bit.

Negative Integers (Two's Complement):

• Negative integers are stored using a method called Two's Complement. In Two's Complement:The leftmost bit (the most significant bit) is used as the sign bit. If this bit is 0, the number is positive, and if it's 1, the number is negative.The remaining bits represent the absolute value of the negative number.To find the Two's Complement of a negative number, you invert all the bits (change 0s to 1s and vice versa) and add 1 to the result.

For example, let's take the decimal number -7:

1. The binary representation of 7 is 0111.
2. To convert it to Two's Complement for -7, we invert all the bits, resulting in 1000.
3. Then, we add 1 to the inverted value, resulting in 1001. This is the Two's Complement representation of -7.

Now, when you perform arithmetic operations with Two's Complement numbers, the hardware is designed to work with them in a way that accounts for the sign bit. This makes it possible to perform addition, subtraction, and other operations on both positive and negative integers using the same hardware.

Two's Complement is a highly efficient and widely used method for representing signed integers in computer memory because it allows for straightforward addition and subtraction while using the same hardware for both positive and negative numbers. It's important to note that the number of bits used to represent integers in memory determines the range of values that can be represented. Larger bit lengths allow for the representation of a wider range of integer values.