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Particularly for highly complex, digital ICs. Is it bottom up or top down? In particular, for top-down design designs the actual logic gates?

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  • \$\begingroup\$ Have you heard of HDLs? And the approach is often mixed. The overall design is top-down. But the lower-level blocks might be designed bottom-up. \$\endgroup\$
    – Eugene Sh.
    Jun 22 '17 at 20:28
  • \$\begingroup\$ Possibly somewhat related: electronics.stackexchange.com/questions/67598/… \$\endgroup\$
    – MarkU
    Jun 22 '17 at 20:46
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Actual logic gates are designed at manufacturer's foundry. They design various gates and other logic elements within their node capabilities, "qualify" their gates, and offer several variants of libraries, for different grade of silicons, low-power, normal, high-performance, etc. So one can say this is "bottom-up".

A customer of a fab (a fabless IC company) designs top-down, from marketing specifications, down to desired functions, integrating various IPs (frequently acquired from big design houses as Synopsis), using an hierarchy of design languages (C#, System Verilog, down to Verilog and VHDL). Then they translate the RTL into offered libraries of a particular FAB.

I hope this answers the original OP question

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