What's a slice in a FPGA ?

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Quick answer - The programmable elements inside a FPGA called CLB = Confiurable Logic Blocks.

If you look inside a CLB will it consist of LUTs = Look Up Table and Flip-Flops/Latches.

The LUTs and F/F's organized in Slices which means that those elements shares connections in order to utilized fast carry chain.

Jeppe
 
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Slices in FPGA

Common components such as flip-flops, LUTs, block RAM, and multiplexers make up the basic logic structures on a FPGA.
A Collection of these basic structures is referred to as a slice or a configurable logic block (CLB). The definitions of a CLB and a slice are specific to each device family.
 

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