[Math] Simplifying a Boolean expression for two-level NAND gate circuits

boolean-algebra

The expression is: F = (X' + Y' + Z')(Y' + A')

I have no clear idea on how to go about simplifying this with Boolean algebra. After it's simplified, I'll need to implement it only using NAND gates.

My instinct is to start off with using the distributive property? Or would it be easier to use k-maps?

Best Answer

First of all, your question is wrong place however your answer is,

$1. \quad F = (X' + Y' + Z')(Y' + A')$

$2. \quad F=(X'Y'+X'A+Y'+Y'A+Z'Y'+Z'A)$

$3. \quad F=( Y'(X'+Z') + A(X'+Z') + Y'(A+1) )$

$4. \quad F=( Y'(X'+Z'+1) + A(X'+Z') )$

$5. \quad F=( Y'(1) + A(X'+Z') )$

$6. \quad F=( Y' + AX' + AZ' )$

Well, How can I draw only NAND gates diagram? Firsty, I have to know that $(AA)'$ is $A'$ and I can obtain not of anything in these question, then you can step back in circuit for correct usage of NANDs.

click here to access circuit

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