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Guys I need to convert an expression using AND, OR and NOT to an expression using only NOR. However I'm not being able to do it algebraically. Can someone give a hint on how to start. I already tried to complement the expression and then to apply De Morgan laws and then complement again.

$ f = \overline{A_3}A_2\overline{A_1} + \overline{A_0}(\overline{A_2} +A_3)$

Jean Marie
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Granger Obliviate
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1 Answers1

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\begin{align} f&=a_3'a_2{a_1}' + a_0'(a_2'+a_3) \\ &=a_3'a_2{a_1}' + a_0'a_2'+a_0'a_3 \\ &=(a_3+a_2'+a_1)' + (a_0+a_2)' + (a_0+a_3')' \\ &=(a_3+(a_2+a_2)'+a_1)' + (a_0+a_2)' + (a_0+(a_3+a_3)')' \\ \end{align}

Explanation:
I tried the way you mentioned (complement, apply De Morgan laws, complement). But, I admit, I didn't apply the rules systematically. When in doubt, you can use the following formulas.

$a'$ becomes $(a+a)'$
$ab$ becomes $((a+a)'+(b+b)')'$
$a+b$ becomes $((a+b)'+(a+b)')'$

blackpen
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