Question

If \( (1235)_x = (3033)_y \), where \( x \) and \( y \) indicate the bases of the corresponding numbers, then

• A. \( 2^8 \)
• B. \( 2^{32} \)
• C. \( 2^{15} \)
• D. \( 2^{19} \)

Hint:

For a memory with \( N \) locations, the number of address lines required is \( \log_2 N \). The number of AND gates required for the decoder corresponds to the number of address lines.

Answer 1

The Correct Option is C

For a memory with \( 32K \times 16 \), the addressing is based on the number of memory locations. Since the memory has 32K locations, we need 15 address lines to address all 32K locations. Therefore, the number of AND gates required for the decoder is \( 2^{15} \), which corresponds to option (C).
Final Answer: (C) \( 2^{15} \)