现代计算机中数字的表示格式及采用的二进制表示标准是什么？

Great question! Since you already have a solid grasp of binary, sign-magnitude, 1's complement, 2's complement, and IEEE 754, let’s dive straight into what modern systems actually rely on for day-to-day operations.

Integer Representation #

• Signed Integers: Two's Complement is the universal standard for signed integer representation in modern general-purpose computers (x86, ARM, RISC-V, etc.). This choice boils down to two key advantages:
  1. It eliminates the ambiguity of "positive zero" and "negative zero" that plagues sign-magnitude and 1's complement.
  2. Addition and subtraction can be implemented with the same hardware circuit—no separate logic needed for subtraction, which simplifies design and boosts efficiency.
• Unsigned Integers: These use straightforward unsigned binary (plain binary without a sign bit), where every bit contributes to the magnitude of the number. This is common for representing counts, memory addresses, and other non-negative values.

Floating-Point Representation #

The global standard for floating-point numbers in modern computing is IEEE 754. It’s used across nearly all systems, from personal computers and servers to embedded devices and GPUs. The two most widely implemented variants are:

• Single-precision (32-bit): Referred to as float in most programming languages.
• Double-precision (64-bit): Referred to as double—this is the default for most floating-point operations due to its higher precision.

While there are extended precision formats (like 80-bit on some x86 systems) and specialized variants for specific use cases (e.g., tensor cores in GPUs), IEEE 754 remains the foundational standard that ensures interoperability between different hardware and software platforms.

A Quick Note on Legacy/Edge Cases #

Rare exceptions exist: some specialized embedded systems, legacy hardware, or niche applications might use sign-magnitude or 1's complement for specific purposes. But these are outliers—for all mainstream computing tasks, two's complement (integers) and IEEE 754 (floats) are the de facto standards.

内容的提问来源于stack exchange，提问作者Bbogdanel71