Assume a computer has the capacity to hold up to 4 memory modules, with each module containing 512M bytes. How many total bits are needed in the memory address?
4×512MB = 2GB = 2^31 bytes. To address any byte requires 31 bits.
To determine the total number of bits needed in the memory address, we need to first calculate the total capacity of the computer's memory.
Given that the computer can hold up to 4 memory modules, and each module has a capacity of 512M bytes, we can calculate the total capacity of the computer's memory as follows:
Total Capacity = Number of Modules × Capacity per Module
Total Capacity = 4 modules × 512M bytes/module
Next, we convert the capacity from bytes to bits, as memory addresses are typically measured in bits. Since there are 8 bits in a byte, we multiply the total capacity by 8:
Total Capacity (in bits) = Total Capacity (in bytes) × 8
Total Capacity (in bits) = (4 modules × 512M bytes/module) × 8
Now, we can calculate the number of bits needed in the memory address. The memory address represents a unique location in the computer's memory, and the number of bits needed is determined by the total capacity of the memory.
To find the number of bits needed, we take the base-2 logarithm (log2) of the total capacity (in bits). The formula for calculating the number of bits needed is as follows:
Number of Bits = log2(Total Capacity (in bits))
Number of Bits = log2[(4 modules × 512M bytes/module) × 8]
Calculating this on a calculator or a programming language, we find:
Number of Bits ≈ log2(16G) ≈ log2(16 × 1024 × 1024 × 1024) ≈ log2(17179869184) ≈ 34 bits
Therefore, the computer would need a total of 34 bits in the memory address to address the full capacity of the 4 memory modules, each containing 512M bytes.