Notes on correct solutions fro h6 (after it was graded).

** #1 Bases **

Converting from base 2, 8, 16 to base 10
- All are basically the same
- Rightmost digit is the 1's digit
- Next rightmost is worth "base"
- Next rightmost after that is worth base**2
- Then base**3
- Etc.
- In bases higher than 10, we need a digit for 10, 11, 12, ....  We use a=10, b=11, c=12, d=13, e=14, f=15

Examples: 2865
5 is the 1's digit, 6 10's digit, 8 10**2's, 2 10**3's
5*1 + 6*10 + 8*10**2 + 2*10**3
2*10**3 + 8*10**2 + 6*10 + 5*1

Example: 101110b
101110b
0 is the 1's digit, 1 is 2's digit, 1 is the 2**2's digit, 1 is the 2**3's digit, 0 is the 2**4's digit, 1 is the 2**5's digit
1*2**5 + 0*2**4 + 1*2**3 + 1*2**2 + 1*2 + 0*1 = 46

Example: 524 base 6
4 is the 1's digit, 2 is 6's digit, 5 is the 6**2's digit
5*6**2 + 2*6 + 4*1


Converting from base 10 to base 2, 8, 16
- All are basically the same
- Two methods
  a) write out powers of base
  b) divide by base, take remainder, repeat - note that this gives the digits in reverse order

Example: 76 decimal, convert to binary
a) write out powers
1, 2, 4, 8, 16, 32, 64, 128
76 = 64 + 12
12 = 8 + 4
76 = 64 + 8 + 4 = 1*64 + 0*32 + 0*16 + 1*8 + 1*4 + 0*2 + 0*1 = 1001100b
But if we convert 76 to base 6
1, 6, 36, 216
76/36 = 2 remainder 4 
76 = 2*36 + 4 = 2*36 + 0*6 + 4*1 = 204 base 6
b) divide by base...
76//2 = 38 remainder 0
38//2 = 19 remainder 0
19//2 = 9 remainder 1
9//2  = 4 remainder 1
4//2  = 2 remainder 0
2//2  = 1 remainder 0
1//2  = 0 remainder 1
76 = 1001100b
Convert 76 to base 6
76//6 = 12 remainder 4
12//6 = 2 remainder 0
2//6  = 0 remainder 2
76 = 204 base 6

Converting between base 2 and base 16 is really easy
- 4 bits of binary corresponds to 1 hexadecimal digit (16 = 2**4)
- pad binary with 0's so each hex digit is exactly 4 bits

Example: convert 1110101110101b to base 16
0001 1101 0111 0101b
 1    14   7    5 hex
 1    E    7    5 hex
 1E75

Example: convert 4bf20 hex to binary
 4    b    f     2   0 hex
0100 1011 1111 0010 0000b


Largest number in base 2, 8, 10, 16 with X digits
- Largest digit in that base repeated X times


** #2 Files and file extensions **

"Magic code"
- Not all file types have something like this
- Those that do have some specific bytes that are always at a set position in the file
- For many of these, it will be the first bytes in the file
- Some "magic codes" are characters so that you could see them by opening the file in a text editor (e.g., open something.pdf in Notepad or TextEdit)
- Others are not, so you have to say what the bits are, or equivalently what the bytes are in hexadecimal
- Some file types have slightly different magic codes depending on the version of the file


** #3 Computer Components **

RAM, CPU, Storage
- Three main parts of the computer
- Note that the CPU has a few different types of "memory" internal to itself
  + CPU registers re the fastest of all, and also the fewest - just a few KB of registers
  + CPU cache is fast memory on the CPU and is broken into levels - L1 is faster than L2 is faster than L3 (and L1 is smaller than L2 is smaller than L3)
- Speed: CPU > RAM > Storage
- Cost per byte: CPU > RAM > Storage
- Size: CPU < RAM < Storage
- Speed of CPU is in GHz
- Speed of RAM is in GHz
- Speed of Storage is often given in MB/s or GB/s