In a 32-bit system, the term “32-bit” refers to the size of the memory addresses that the system uses to access and reference different locations in its memory. Each memory address in a 32-bit system is represented by 32 binary digits (bits). The number of bits in an address determines the total addressable memory space of the system.
To understand why a 32-bit system can address a maximum of 4 GB (gigabytes) of memory, we need to examine how binary numbers and memory addressing work.
In binary representation, each bit can have two possible states: 0 or 1. A single bit can represent 2 different values (2·1). For example:
- 0 (binary: 0) and 1 (binary: 1)
Similarly, with 2 bits, we can represent 2·2 = 4 different values:
- 00 (binary: 0)
- 01 (binary: 1)
- 10 (binary: 2)
- 11 (binary: 3)
Extending this pattern, with 3 bits, we can represent 2·3 = 8 different values, and with 4 bits, we can represent 2·4 = 16 different values, and so on.
Now, in a 32-bit system, there are 32 bits in each memory address. So, the total number of unique addresses that can be represented in this system is 2·32.
Let’s calculate that: 2·32 = 4,294,967,296
The value 4,294,967,296 represents the total number of unique memory addresses that can be used in a 32-bit system. Each address points to a single byte of memory. Since 1 gigabyte (GB) is equal to 1,073,741,824 bytes, we can convert the number of addresses into gigabytes:
4,294,967,296 bytes ÷ 1,073,741,824 bytes per GB ≈ 4 GB
Therefore, a 32-bit system can address a maximum of approximately 4 GB of memory. This is why 32-bit operating systems are limited in their ability to access and utilize memory beyond this 4 GB limit. To address more memory, one would need to move to a 64-bit system, which uses 64-bit memory addresses and can access significantly larger amounts of memory