Microcode in Intel's 8087 floating-point chip: the scale instruction

Ken Shirriff explores the intricate microcode architecture of the Intel 8087, the pioneering math coprocessor for the 8086 CPU. The article focuses on the 'scale' instruction, which performs rapid multiplication by powers of two by manipulating the exponent of a floating-point number. By reverse-engineering the chip's internal microcode, Shirriff reveals how the 8087 handles exponent adjustments and normalization. The analysis provides a rare look at how early floating-point arithmetic was implemented at the hardware level, highlighting the clever bit-manipulation techniques used to optimize performance in an era of limited transistor counts. This deep dive into the 8087's control store offers valuable insights for computer architecture enthusiasts and historians, demonstrating how complex mathematical operations were distilled into efficient sequences of micro-instructions within the silicon.