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Implementing a Function Using Look-Up Tables

Thread starter Vishera
Start date Oct 21, 2014
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Function

1 reply · 1K views · last reply Oct 21, 2014

Vishera

Thread starter
Oct 21, 2014

#1

Homework Statement

Homework problem text: Implement the 3-input XOR function f(x1, x2, x3) = x1 ⊕ x2 ⊕ x3 using only two 2-input look-up-table (2-LUTs). Draw the circuit and identify the LUT inputs. Hint: Shannon's Exp. Theorem

Homework Equations

The Attempt at a Solution

I am unsure how to proceed from here. Here is what I understand LUTs to look like:

Truth table for f1 of inputs x1 and x2 next to a LUT diagram: storage cells hold 1, 0, 0, 1 feeding two multiplexers driven by x2, and a final multiplexer selected by x1 outputs f1.

Here is my attempt so far:
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Handwritten derivation on lined paper of f(x1, x2, x3) = x1 XOR x2 XOR x3 implemented with 2-input LUTs, using Shannon expansion into g = x2 NOT x3 and h = x2 x3 with subterms k and m.

Handwritten circuit sketch of a multiplexer-based lookup table: input x3 feeds the select of a 2-to-1 mux whose inputs come from small 1 and 0 cells, with a second mux labelled 3 below and output lines K and 3 on the right.

Discussion

Vishera

Oct 21, 2014

#2

Do LUTs need to look exactly like this below? Or can LUTs be any sort of box that has 2 inputs and 1 output?

Also, do LUTs need those pink squares? i.e. stored 1's and 0's inside the LUT as memory.

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