COMP-200: Intro to Computer Systems

Assignment 2

mo khan - 3431709

Choose ONE exercise each from Chapters 4 and 5

Chapter 4:

| Base (N) | N^8         | N^7        | N^6       | N^5    | N^4   | N^3 | N^2 | N^1 |
| ----     | -           | -          | -         | -      | -     | -   | -   | -   |
| 2        | 128         | 64         | 32        | 16     | 8     | 4   | 2   | 1   |
| 4        | 16,384      | 4,096      | 1,024     | 256    | 64    | 16  | 4   | 1   |
| 8        | 2097152     | 262144     | 32768     | 4096   | 512   | 64  | 8   | 1   |
| 10       | 10,000,000  | 1,000,000  | 100,000   | 10,000 | 1,000 | 100 | 10  | 1   |
| 16       | 268,435,456 | 16,777,216 | 1,048,576 | 65,536 | 4,096 | 256 | 16  | 1   |

8.times.map { |x| 2**x }.reverse
=> [128, 64, 32, 16, 8, 4, 2, 1]
8.times.map { |x| 4**x }.reverse
=> [16384, 4096, 1024, 256, 64, 16, 4, 1]
8.times.map { |x| 8**x }.reverse
=> [2097152, 262144, 32768, 4096, 512, 64, 8, 1]
8.times.map { |x| 10**x }.reverse
=> [10000000, 1000000, 100000, 10000, 1000, 100, 10, 1]
8.times.map { |x| 16**x }.reverse
=> [268435456, 16777216, 1048576, 65536, 4096, 256, 16, 1]

Given our discussion of positional numbering systems in Section 4.2.1, see whether you can determine the decimal value of the following numbers:

a. 133 (base 4) = 31 (base 10)

  ```plaintext
  | 64 | 16 | 4 | 1 |
  | -- | -- | - | - |
  | 0  | 1  | 3 | 3 |
  ```

  ```ruby
  (1*16) + (3*4) + (3*1)
  => 31
  31.to_s(4)
  => "133"
  ```

b. 367 (base 8, also called octal) = 247 (base 10)

  ```plaintext
  | 512 | 64 | 8 | 1 |
  | --- | -- | - | - |
  |   0 | 3  | 6 | 7 |
  ```

  ```ruby
  (3*64) + (6*8) + (7*1)
  => 247
  247.to_s(8)
  => "367"
  ```

c. 1BA (base 16, also called hexadecimal. B is the digit that represents 11; A is the digit that represents 10.) = 442 (base 10)

  ```plaintext
  | 4,096 | 256 | 16 |  1 |
  | ----- | --- | -- | -- |
  |     0 |   1 |  B |  A |
  |     0 |   1 | 11 | 10 |
  ```

  ```ruby
  (1*256) + (11*16) + (10*1)
  => 442
  442.to_s(16)
  => "1ba"
  ```

Chapter 5:

A memory unit that is said to be 640 KB would actually contain how many memory cells? What about a memory of 512 MB? What about a memory of 2 GB?

The standard cell size of each member cell is 8 bits or 1 byte.
```
| Value  | Bytes         |
| -----  | -----         |
| 640 KB | 655,360       |
| 512 MB | 536,870,912   |
| 2 GB   | 2,147,483,648 |
```