The Boolean function Y = AB + CD is to be realized using only two-input NAND gates. The minimum number of gates required are:

Concept:

De Morgan’s law states that:

\(\overline {\left( {{A_1}\;.\;{A_2} \ldots \;{A_n}} \right)} \; = \left( {\overline {{A_1}} \; + \;\overline {{A_2}} \; + \; \ldots \; + \;\overline {{A_n}} } \right)\;\)

\(\overline {\left( {{A_1}\; + \;{A_2}\; + \; \ldots \; + \;{A_n}} \right)} \; = \left( {\overline {{A_1}} \;.\;\overline {{A_2}} \;.\;..\;\overline {{A_n}} } \right)\)

Analysis:

\(\begin{array}{l} y = AB + CD\\ = \overline {\overline {AB + CD} } \\ = \overline {\overline {AB} .\overline {CD} } \end{array}\)

Only 3 NAND gates are required