Final answer:
The number of bits required to address a 1M × 8 main memory is approximately 20 bits, as 2 to the power of 20 is 1,048,576, which covers a memory size of 1,000,000 bytes. None of the options provided correctly states the number of bits required. The closest correct answer would be slightly more than 1 megabit.
Step-by-step explanation:
To determine how many bits are required to address a 1M × 8 main memory, we first need to understand what this specification means. 1M indicates 1 megabyte (MB) of memory, which can hold one million bytes. Since memory addresses typically point to bytes rather than bits, we are addressing 1,000,000 bytes in this case.
Memory addressing is based on binary numbers, and the number of address lines needed is determined by the number of unique locations needed. To calculate the number of bits needed to address each byte in memory, we use the formula: 2n = Number of addresses, where n is the number of bits.
To find n, we take the logarithm base 2 of the number of memory locations, which is 1,000,000 (since we're considering 1M). Mathematically:
n = log2(1,000,000)
After performing the calculation, we find that n is approximately 20. Therefore, we need 20 bits to address a 1M × 8 main memory. None of the options provided (A: 1 megabit, B: 8 megabits, C: 1 kilobit, D: 8 kilobits) correctly states the number of bits required. The correct answer would be slightly more than 1 megabit (since 1 megabit = 220 bits = 1,048,576 bits) but less than any of the other options provided.
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