In binary, normalized numbers are represented as $\pm 1.xxxxxxx_2 \times 2^{yyyy}$.

Why normalization?

• Unique representation: only use one way to represent
• Maximize precision: useless leading zeros waste space
• Standards

Floating-Point: IEEE 754-1985 standard → Single precision (32-bit), Double precision (64-bit)

(1 + fraction) is called the significand

• Why is the exponent in the floating point format not a 2’s complement nor a signed magnitude but a biased representation?

Compared to Fixed-Point Numbers, Floating point number system can cover a much more extensive range!

Floating-Point Addition:

在现代流水线处理器中，单精度浮点加法的典型延迟（Latency）通常为4个时钟周期。

• FP multiplier is of similar complexity to FP adder
• FP和integer division都很难pipeline，同时，conversion unit也很难