How are integers represented in memory?

Integers are represented in memory as binary numbers, using a system known as two's complement.

In computer systems, integers are stored in memory as binary numbers, which are a series of 1s and 0s. The most common way to represent these integers is through a system known as two's complement. This system allows for the representation of both positive and negative integers, making it a versatile choice for many computing applications.

The size of the integer that can be stored depends on the number of bits allocated for that integer. For example, an 8-bit integer can store values from -128 to 127, a 16-bit integer can store values from -32,768 to 32,767, and so on. The range of values is determined by the formula -2^(n-1) to 2^(n-1) - 1, where n is the number of bits.

In the two's complement system, the sign of the integer is determined by the most significant bit (MSB). If the MSB is 0, the number is positive, and if it is 1, the number is negative. For positive numbers, the binary representation is straightforward. However, for negative numbers, the process is a bit more complex. The binary representation of a negative number is obtained by inverting the bits of its absolute value and then adding 1 to the result.

For example, to represent -9 in an 8-bit two's complement system, you would first represent 9 as 00001001. Then, you would invert the bits to get 11110110. Finally, you would add 1 to get 11110111, which is the representation of -9.

This system of representing integers in memory is widely used because it simplifies the hardware design of the computer. With two's complement, the same circuitry can be used to perform both addition and subtraction, which makes the design of the computer simpler and more efficient.