Assume a computer system with 4Kx16 bits of RAM. Design using RAM chips of 256x8.
a) How many memory chips are needed?
b) How many address lines are needed to access any word in the total memory?
c) How many address lines are common to all chips?
d) How many address lines must be decoded for chip select?
e) What is the size of the decoder?
Answer (2)
Calculate the number of chips needed: 256 × 8 4 K × 16 = 32 .
Determine the number of address lines for total memory: 2 n = 4096 , so n = 12 .
Determine the number of common address lines: 2 m = 256 , so m = 8 .
Calculate the number of address lines for chip select: 12 − 8 = 4 .
The size of the decoder is 4-to-32. Therefore, the answers are: a) 32 chips b) 12 address lines c) 8 address lines d) 4 address lines e) 4 − t o − 32 decoder
Explanation
Problem Analysis We are given a computer system with 4Kx16 bits of RAM, and we need to design it using RAM chips of 256x8 bits. We need to find the number of chips needed, the number of address lines, the number of common address lines, the number of address lines for chip select, and the size of the decoder.
Calculating Total Bits First, let's calculate the total number of bits in the RAM: Total RAM size in bits = 4K x 16 = 4096 x 16 = 65536 bits. Next, let's calculate the number of bits per RAM chip: RAM chip size in bits = 256 x 8 = 2048 bits.
Calculating Number of Chips Now, we can calculate the number of chips needed: Number of chips = Total RAM size in bits / RAM chip size in bits = 65536 / 2048 = 32 chips.
Address Lines for Total Memory To determine the number of address lines needed to access any word in the total memory, we know the total memory has 4K words, which is 4096 words. We need to find n such that 2 n = 4096 . Since 2 12 = 4096 , we need 12 address lines.
Common Address Lines To determine the number of address lines required to address a single RAM chip, we know each chip has 256 words. We need to find m such that 2 m = 256 . Since 2 8 = 256 , we need 8 address lines. These address lines are common to all chips.
Address Lines for Chip Select To calculate the number of address lines that must be decoded for chip select, we subtract the number of address lines common to all chips from the total number of address lines: 12 - 8 = 4 address lines.
Decoder Size Finally, to determine the size of the decoder, we know the decoder takes the chip select address lines as input and generates a unique output for each chip. We have 4 input lines and 32 output lines (since we have 32 chips). Therefore, the size of the decoder is 4-to-32.
Final Answer In summary: a) The number of memory chips needed is 32. b) The number of address lines needed to access any word in the total memory is 12. c) The number of address lines common to all chips is 8. d) The number of address lines that must be decoded for chip select is 4. e) The size of the decoder is 4-to-32.
Examples
Consider a scenario where you're designing a memory system for a simple embedded device. Understanding how to calculate the number of memory chips, address lines, and decoder size is crucial for efficient memory management. For instance, if you're building a system that stores sensor data, you need to ensure you have enough memory and can access it quickly. The calculations we performed help determine the hardware requirements for such a system, ensuring it operates correctly and efficiently. This knowledge is also foundational for understanding more complex memory architectures in larger computer systems.
A total of 32 memory chips are required for the system, with 12 address lines needed to access the total memory. Among these, 8 address lines are common to all chips, and 4 address lines must be decoded for chip selection. The decoder required for this system is a 4-to-32 type.
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