Friday, June 26, 2009

practice problems for changing bases

1) Change FADhex into decimal.

2) Change FADhex into binary.

3) Change 1,776dec into hexadecimal.

4) Change 1,776dec into binary.

5) Change 110 0101 0000 0110bin into hexadecimal.

6) Change 110 0101 0000 0110bin into decimal.

Answers in the comments.

3 comments:

Anonymous said...

seems like the question you were meaning to ask in #6 was change 110 0101 0000 0110bin to decimal not hex. Is that correct?

Prof. Hubbard said...

The anonymous poster above is correct. Problem 6 is supposed to be from binary to decimal. The post has been changed and the answers are here.

1) Change FAD(hex) into decimal.

FAD(hex)
Answer = 15
AD(hex)
Answer = 16*15 + 10 = 250
D(hex)
Answer = 16*250 + 13 = 4,013(dec)

2) Change FAD(hex) into binary.

Using the table look-up, the answer is 1111 1010 1101(bin).

3) Change 1,776(dec) into hexadecimal.

1776/16 = 111 remainder 0
Answer = 0
111/16 = 6 remainder 15 (F)
Answer = F0
Since 6 is less than 16, we get
Answer = 6F0(hex).

4) Change 1,776(dec) into binary.

Again, table look-up of the hexadecimal is the easiest way to solve this.

1,776(dec) = 0110 1111 0000(bin)

5) Change 110 0101 0000 0110(bin) into hexadecimal.

Answer: Using the table look-up, we get 6506(hex).

6) Change 110 0101 0000 0110(bin) into decimal.

Answer: It's easier to change the hexadecimal version from problem 5.

6506(hex)
Answer = 6
506(hex)
Answer = 16*6 + 5 = 101
06(hex)
Answer = 16*101 = 1,616
6(hex)
Answer = 16*1,616+6 = 25,862(dec)

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