# How to derive the boolean expression of a multi-bit gate

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## How to derive the boolean expression of a multi-bit gate

 In Unit 1.2 we were given a method to derive the boolean expression of a simple 1 bit input-1 bit output truth table - ANDing together the inputs for each line that outputs 1, and ORing them together. I found that method to be very useful in finding the expression for, say, a Mux or Dmux gate. However I'm having trouble in deriving the boolean expression for multi-bit gates, like a Mux4Way16. Is this method relevant at all when dealing with multi-bit gates? If it is, how do you do it?
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## Re: How to derive the boolean expression of a multi-bit gate

 Administrator You can derive the canonical representation for Mux4Way (1-bit) and Mux8Way, and then replicate them 16 times. You will find that the implementations for the one bit versions will be rather big because they have And terms that are 3 and 4 inputs wide and Or terms that are 4 and 8 inputs wide. For Nand2Tetris, think about the strategy "what did I just build and how can I use it to build the next thing." In the case of Mux4Way16, you can build it out of 3 Mux16. Think about the symbol for Mux4Way16 and how you can draw 3 Mux16 inside it. --Mark