关于Fixed point、Floating point等四种数值表示术语的疑问咨询

Hey there! Let's break down these four terms with super simple examples so everything clicks—no jargon overload, promise.

These are just markers that split a number into its integer and fractional parts—they're not full number representation systems, just symbols.

Decimal Point（小数点） #

You use this every day! It's the dot in numbers like 3.14 or 100.5. Left of the dot is whole numbers (ones, tens, hundreds...), right is fractions (tenths, hundredths...). Super straightforward.

Binary Point（二进制点） #

Think of this as the binary version of the decimal point. In binary (base-2) numbers, it splits the integer and fractional parts of a binary number. For example:

• Binary 10.1 translates to decimal 2.5 (left of the point: 10 = 2; right: 1 = 0.5).
  Just like the decimal point, it's just a separator—nothing more, nothing less.

These are two ways computers (or we) can represent numbers, using the points above.

Fixed Point（定点数） #

The core rule here: the position of the binary/decimal point is fixed, no matter what number you're representing. We all agree on where the point lives upfront, and every number follows that rule.

Example time: #

Let's say we make a rule: "All numbers will have exactly 2 binary fractional digits"—so the binary point sits 2 places from the right.

• The integer 2 in binary is 10. To fit our fixed-point rule, we write it as 10.00 (we add two zeros to keep the point in the fixed spot).
• A fractional number like 0.5 (binary 0.1) becomes 00.10 (we pad with a leading zero to keep the point in place).

Your question about integer 2: #

Yes, 2 absolutely counts as a fixed-point number! If we set our rule to "no fractional digits" (point sits right after the integer part), then 2's fixed-point form is just binary 10 (or decimal 2). The key is that the point's position doesn't change—even for whole numbers, we're still following the fixed rule.

When to use fixed point: #

Great for situations where you need exact precision and your numbers stay within a predictable range. Think embedded systems (like sensor readings) or financial calculations (where you can't afford tiny rounding errors).

Floating Point（浮点数） #

Here's the opposite of fixed point: the binary/decimal point can "float" around—we use a scientific notation-style approach to represent super big or super small numbers without wasting space.

Example time: #

Take the integer 2 again. In binary scientific notation, we write it as 1.0 × 2^1. Here, we moved the binary point from after the 10 (10.) to after the first 1 (1.0), then use the exponent 1 to track how far we moved the point.

In computers, floating-point numbers have a standard structure (like 32-bit single precision): a sign bit (positive/negative), an exponent (to track the point's position), and a mantissa (the main digits of the number). For 2, that translates to a sign bit of 0 (positive), exponent of 128 (since we add an offset to make exponents non-negative), and mantissa of 0. But you don't need to memorize that—just remember the "floating point = movable point + exponent" idea.

Your questions about 2: #

• Can 2 be represented as floating point? Absolutely! As we saw, it's 1.0 × 2^1 in binary floating point, or 2.0 × 10^0 in decimal floating point.
• Can 2 use a binary point? Yep—you can write it as 10. or 10.0 in binary, which includes the binary point. This is just the binary representation of 2 with the point explicitly marked; it can be part of a fixed-point or floating-point system.

• Decimal/Binary Point: Just separators for integer/fractional parts in their respective bases.
• Fixed Point: Fixed point position, exact precision, limited range.
• Floating Point: Movable point position, wide range, small precision tradeoffs (most numbers are approximations).

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