Module 4: Part II

Number Systems

Take the original value and divide by 2
- Continue dividing each quotient by 2 until you end up with 0.5
- Remainder of each division by 2 is the bit that goes in the 0, 1, 2, 3 place and so on
Ex:
- Convert 13 to binary
- 13/2 = 6 with remainder of 1 (1 in zero place)
- 6/2 = 3 with remainder of 0 (0 in ones place)
- 3/2 = 1 with remainder of 1 (1 in twos place)
- ½ = 0 with remainder of 1 (1 in threes place)
- 13 in binary is 1101
Ex 2:
- Convert 422 to binary
- 422/2 = 211 remainder 0 (zeros place)
- 211/2 = 105 remainder 1
- 105/2 = 52 remainder 1
- 52/2 = 26 remainder 0
- 26/2 = 13 remainder 0
- 13/2 = 6 remainder 1
- 6/2 = 3 remainder 0
- 3/2 = 1 remainder 1
- ½ = 0 remainder 1
- 422 in binary = 0b110100110

How many times does a power of 16 fit into our value?
16^0 = 1, 16^1 = 16, 16^2 = 256, 16^3 = 4096, 16^4 = 65536, 16^5 = 1038577 and so on…
Ex: Convert 9742 from decimal to hexadecimal
- start with the largest multiple of 16 that can fit into our original numbers
- How many times can 4096 fit into 9742? Two times
  - So, the fourth value in our answer is 2 (working from left to right)
  - 4096 contributes to our overall value twice
  - 9742 - 4096(2) = 1550
- Then, we move down the powers of 16
- How many times can 256 fit into 1550? Six times
  - So, the third value in our answer is 6 (working from left to right)
  - 1550 - 256(6) = 14
- Then, we move down the powers of 16
- How many times can 16 fit into 14? Zero times
  - So, the second value in our answer is 0 (working from left to right)
  - No subtraction since 16 did not contribute to our total value
- Then, we move down the powers of 16
- How many times can 1 fit into 14? 14 times
  - So, the first value in our answer is E (in hexadecimal) (working from left to right)
  - Final answer: 9742 in hexadecimal = 0x260E

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