GATE EC 2016 Set 2 — Question 52
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Digital Circuits → Combinational Logic → Boolean Algebra & Identities
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Question
An 8 Kbyte ROM with an active low Chip Select input () 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 to , where is the most significant address bit. Which one of the following logic expressions will generate the correct signal for this ROM?
Correct answer
(A) A₁₅ + A₁₄ + (A₁₃ · A₁₂ + A₁₃ · A₁₂)
Solution
1.The address range is 1000H to 2FFFH. In binary, this corresponds to:
- 1000H:
- 2FFFH:
3.The selection condition is true when and . Thus, .
4.Since is active low, .
5.Applying De Morgan's law: .
6.The complement of XOR is XNOR: .
7.Therefore, , which matches option (A).
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