The maximum memory size of microprocessors of different generations are given at Table 1.2. Represent each of the memory size in terms of power of 2.

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Accepted Answer

> [!TLDR]
> Table 1.2's maximum memory sizes, written as powers of 2 (bytes): 1 KB = 2^10 B, 1 MB = 2^20 B, 16 MB = 2^24 B, 4 GB = 2^32 B, 64 GB = 2^36 B.

**The idea.** Memory sizes come out as powers of 2 because a processor with n address lines can address exactly 2^n memory locations. The unit ladder itself is built on powers of 2:

```text
1 KB = 1024 B = 2^10 B      1 MB = 2^20 B      1 GB = 2^30 B
```

**Working each generation's maximum memory size from Table 1.2:**

| Generation | Maximum memory | As bytes | Power of 2 |
|---|---|---|---|
| First (1971-73) | 1 KB | 1024 B | 2^10 B |
| Second (1974-78) | 1 MB | 1024 x 1024 B | 2^20 B |
| Third (1979-80) | 16 MB | 2^4 x 2^20 B | 2^24 B |
| Fourth (1981-95) | 4 GB | 2^2 x 2^30 B | 2^32 B |
| Fifth (1995 till date) | 64 GB | 2^6 x 2^30 B | 2^36 B | …

Unit	Abbreviation	Binary Value (common in RAM/OS)	Decimal Value (common in hard drives)
Byte	B	8 bits	8 bits
Kilobyte	KB	$2^{10} = 1024$ bytes	$10^3 = 1000$ bytes
Megabyte	MB	$2^{20} = 1,048,576$ bytes	$10^6 = 1,000,000$ bytes
Gigabyte	GB	$2^{30} = 1,073,741,824$ bytes	$10^9 = 1,000,000,000$ bytes
Terabyte	TB	$2^{40} \approx 1.1 \times 10^{12}$ bytes	$10^{12} = 1,000,000,000,000$ bytes

Q.The maximum memory size of microprocessors of different generations are given at Table 1.2. Represent each of the memory size in terms of power of 2.

Concept understanding — Digital Storage Units

Digital Storage Units: From Intuition to Precision

How to remember the order

Generation	Maximum memory	Power of 2
First	1 KB	2^10 B
Second	1 MB	2^20 B
Third	16 MB	2^24 B
Fourth	4 GB	2^32 B
Fifth	64 GB	2^36 B

Generation	Maximum memory	As bytes	Power of 2
First (1971-73)	1 KB	1024 B	2^10 B
Second (1974-78)	1 MB	1024 x 1024 B	2^20 B
Third (1979-80)	16 MB	2^4 x 2^20 B	2^24 B
Fourth (1981-95)	4 GB	2^2 x 2^30 B	2^32 B
Fifth (1995 till date)	64 GB	2^6 x 2^30 B	2^36 B

Q.The maximum memory size of microprocessors of different generations are given at Table 1.2. Represent each of the memory size in terms of power of 2.

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