Suppose you want to build a memory with 4 byte words and a capacity of $2^{21}$ bits. What is type of decoder required if the memory is built using $2\text{ K} \times 8$ RAM chips?
- A. 5 to 32
- B. 6 to 64
- C. 4 to 16
- D. 7 to 128
Answer: A. 5 to 32
Explanation: Total Capacity = $2^{21}$ bits = $2$ Megabits.\nWord size = 4 bytes = 32 bits.\nNumber of words = $2^{21} / 32 = 2^{16}$ words = $64\text{ K}$ words.\nChips: $2\text{ K} \times 8$.\nTo make 32-bit width, we need 4 chips in parallel ($4 \times 8 = 32$).\nTo make $64\text{ K}$ depth, we need $64\text{ K} / 2\text{ K} = 32$ rows.\nWe need to select 1 out of 32 rows. This requires a $5 \times 32$ decoder.