The following RAM chips are specified by the number of words times the number of bits per word. For each, specify:
a. The number of address lines needed for each memory chip
b. The number of data lines needed for each memory chip
c. The number of bytes that can be stored in each memory chip (note that there are 8 bits/byte)
128 KB words x 8 bits/word
512 KB words x 16 bits/word
512 MB words x 32 bits/word
8 GB words x 64 bits/word
Address lines are required to address each word. For n lines, the number of possible address is 2^n addresses.
For 128K words, there are 2^7 addresses, so 7 address lines are required.
Each word has a width of 8 bits, so to address each bit individually (and internally), 8 lines are required.
The storage is
128K x 8bits
= 128K * 1 byte
= 128*2^10 bytes
= 131072 bytes
So answer for the first case is 7 address lines, 8 data lines and 131072 bytes.
The remaining cases are similar.
address lines is reqired in 512 k word memory
To determine the number of address lines, data lines, and the number of bytes that can be stored in each memory chip, we need to use the following formulas:
a. Number of Address Lines = log2(Number of Words)
b. Number of Data Lines = Number of Bits per Word
c. Number of Bytes = (Number of Words * Number of Bits per Word) / 8
Let's calculate for each memory chip:
1. For 128 KB words x 8 bits/word:
a. Number of Address Lines = log2(128 KB) = log2(128 * 1024) ≈ log2(131,072) ≈ 17
b. Number of Data Lines = 8 bits/word = 8
c. Number of Bytes = (128 KB * 8 bits/word) / 8 = (128 * 1024 * 8) / 8 = 128 * 1024 = 131,072 bytes
2. For 512 KB words x 16 bits/word:
a. Number of Address Lines = log2(512 KB) = log2(512 * 1024) ≈ log2(524,288) ≈ 19
b. Number of Data Lines = 16 bits/word = 16
c. Number of Bytes = (512 KB * 16 bits/word) / 8 = (512 * 1024 * 16) / 8 = 1,048,576 bytes
3. For 512 MB words x 32 bits/word:
a. Number of Address Lines = log2(512 MB) = log2(512 * 1024 * 1024) ≈ log2(536,870,912) ≈ 29
b. Number of Data Lines = 32 bits/word = 32
c. Number of Bytes = (512 MB * 32 bits/word) / 8 = (512 * 1024 * 1024 * 32) / 8 = 2,147,483,648 bytes
4. For 8 GB words x 64 bits/word:
a. Number of Address Lines = log2(8 GB) = log2(8 * 1024 * 1024 * 1024) ≈ log2(8,589,934,592) ≈ 33
b. Number of Data Lines = 64 bits/word = 64
c. Number of Bytes = (8 GB * 64 bits/word) / 8 = (8 * 1024 * 1024 * 1024 * 64) / 8 = 68,719,476,736 bytes
So, the results for each memory chip are as follows:
1. 128 KB words x 8 bits/word:
a. Number of Address Lines = 17
b. Number of Data Lines = 8
c. Number of Bytes = 131,072 bytes
2. 512 KB words x 16 bits/word:
a. Number of Address Lines = 19
b. Number of Data Lines = 16
c. Number of Bytes = 1,048,576 bytes
3. 512 MB words x 32 bits/word:
a. Number of Address Lines = 29
b. Number of Data Lines = 32
c. Number of Bytes = 2,147,483,648 bytes
4. 8 GB words x 64 bits/word:
a. Number of Address Lines = 33
b. Number of Data Lines = 64
c. Number of Bytes = 68,719,476,736 bytes