How many numbers and characters are represented in computer memory?

Answer 1

Since binary only has two binary digits (0 or 1), then for a 32-bit address space (4GB of memory total) there is an absolute maximum of 34,359,738,368 possible values in the range 0 to 1, inclusive, and an absolute minimum of 1 value in the unsigned range 0 to 234,359,738,368-1, inclusive.

There's no real point in discussing how many characters are represented, since digital computers only store numeric data, not characters. It's the programs you run that determine what each numeral actually represents -- the actual data -- whether it be a signed value, an unsigned value, a floating point value, a character code, or some other form of data altogether, all of which must be digitised (encoded in binary).

If we ignore the fact that additional memory is required to store a character map, including the font that describes each character (digitally) and maps it to a character code (the actual data value), along with the machine code required to actually generate the bitmap of the character, not to mention the operating system and all its required services, then you could have a maximum of 4,294,967,296 8-bit characters or 2,147,483,648 16-bit characters in a 32-bit address space. The actual maximum will be substantially lower but it is impossible to calculate definitively as it is wholly-dependent upon the actual available memory out of the 4GB address space.

64-bit systems have, to all intents and purposes, unlimited capacity for memory, supporting far more memory than physically exists on the planet for one 64-bit machine, never mind all of them at once. So much so that even if you were able to buy 1GB of RAM every single second from now onwards, it would take you over 500 years to fill the machine to capacity, by which time it will have been rendered obsolete 100 times over if it isn't crushed under the weight of its own RAM. In reality, no motherboard can possibly support that amount of memory and they never will. As time progresses, the upper limit will gradually increase but, sooner or later, the laws of physics will dictate the upper ceiling. For now, since the upper ceiling is an entirely unknown quantity, it's impossible to say exactly how many values can be stored in memory. Whatever it is, it's a safe bet to say it'll be more than enough for anyone's needs.

Answer 2

In computer memory, numbers and characters are represented using binary notation, which consists of sequences of 0s and 1s. Here is a detailed explanation of how many numbers and characters can be represented:

Numbers

Binary Representation

Bits and Bytes: A bit is the smallest unit of memory and can be either 0 or 1. A byte consists of 8 bits.

Range of Numbers: The number of bits determines the range of numbers that can be represented. For example, an 8-bit system can represent $$2^8 = 256$$ different values, ranging from 0 to 255 for unsigned integers, or -128 to 127 for signed integers using two's complement representation.

Examples

4-byte (32-bit) Integer: Can represent numbers from 0 to $$2^{32} - 1 = 4,294,967,295$$ for unsigned integers.

Floating Point Numbers: Represented using a combination of bits for the sign, exponent, and mantissa. For example, a 32-bit floating point number (single precision) uses 1 bit for the sign, 8 bits for the exponent, and 23 bits for the mantissa.

Characters

Character Encoding Systems

ASCII (American Standard Code for Information Interchange): Uses 7 bits to represent 128 characters, including letters, digits, and control characters. Extended ASCII uses 8 bits to represent 256 characters.

Unicode: A more comprehensive encoding system that can represent over 65,000 characters using 16 bits (Basic Multilingual Plane) and over a million characters with supplementary planes. Unicode is designed to cover all characters from all writing systems.

Examples

ASCII: The character 'A' is represented by the binary value 01000001, which corresponds to the decimal value 65.

Unicode: Can represent characters from various languages, including special symbols and emojis, using a combination of 16-bit and 32-bit encoding.