Integers are represented in computer memory using a binary system, where each digit is a bit (0 or 1). This system is efficient because it aligns with the way computers process information.
Here's a breakdown of the process:
1. Binary Representation:
- Integers are converted to their binary equivalent. For example, the decimal number 10 is represented as 1010 in binary.
- Each digit in the binary representation represents a power of 2.
- The rightmost digit represents 2<sup>0</sup> (1), the next digit represents 2<sup>1</sup> (2), and so on.
2. Memory Allocation:
- Computers allocate a specific number of bits to store an integer. This allocation depends on the data type and the programming language used.
- Common sizes include 8 bits (byte), 16 bits, 32 bits, and 64 bits.
3. Sign Representation:
- To represent both positive and negative integers, a sign bit is used. The leftmost bit is usually designated as the sign bit.
- A 0 in the sign bit indicates a positive number, while a 1 indicates a negative number.
4. Two's Complement:
- Negative numbers are typically represented using two's complement.
- This method involves inverting all the bits in the binary representation of the positive number and adding 1.
- For example, the two's complement of 5 (00000101) is -5 (11111011).
5. Memory Address:
- Each integer is stored at a unique memory address, allowing the computer to access it easily.
Example:
Let's say we want to represent the decimal number 10 in memory using a 16-bit system:
- Binary Conversion: 10 in decimal is 1010 in binary.
- Padding: Since we have a 16-bit system, we need to add leading zeros to the binary representation: 0000000000001010.
- Memory Allocation: This binary representation would be stored at a specific memory address.
By understanding these steps, you can grasp how integers are represented and manipulated within a computer's memory.
