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An $8$ Kbyte ROM with an active low Chip Select input $\left (\overline{CS}\right )$ is to be used in an $8085$ microprocessor based system. The ROM should occupy the address range $1000H$ to $2FFFH$. The address lines are designated as $A_{15}$ to $A_{0}$, where $A_{15}$ is the most significant address bit. Which one of the following logic expressions will generate the correct $\overline{CS}$ signal for this ROM?

  1. $A_{15}+ A_{14}+\left ( A_{13} \cdot A_{12}+\overline{A_{13}} \cdot \overline{A_{12}} \right )$
  2. $A_{15} \cdot  A_{14} \cdot (A_{13}+A_{12})$
  3. $\overline{A_{15}} \cdot \overline{A_{14}} \cdot  \left ( A_{13}.\overline{A_{12}}+\overline{A_{13}} \cdot A_{12} \right )$
  4. $\overline{A_{15}}+ \overline{A_{14}}+A_{13} \cdot A_{12}$
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