Homework 1 Due at the start of class Wednesday, September 17, 2003.





Show your work on Problems 1 to 12.

Problem 1.
Convert $245_7$ to a base 10 number.

Problem 2.
Convert $245_{10}$ to a base 7 number.

Problem 3.
Convert $324_{6}$ to a base 4 number.

Problem 4.
Convert $100011101_2$ to octal.

Problem 5.
Convert $11010001101001_2$ to hexadecimal.

Problem 6.
Convert $3720623_8$ to hexadecimal.

Problem 7.
Add $\mbox{B13A9E4CA}_{16} ~+~ \mbox{8DB9FC5A2}_{16}$.

Problem 8.
Subtract $\mbox{B13A9E4CA}_{16} ~-~ \mbox{8DB9FC5A2}_{16}$.

Problem 9.
Convert $11.101_2$ to decimal notation.

Problem 10.
Convert $1.101101101\overline{101}_2$ to decimal notation.

Problem 11.
Convert $0.45_{10}$ to binary notation (with a binary point).

Problem 12.
Convert $0.16666\overline{6}_{10}$ to binary notation (with a binary point).




Problem 13.
(a)
Show that if the sum of the digits of a number (in base 10) is divisible by 9 then the original number is also divisible by 9. HINT: Use mod 9.
(b)
Show that if the sum of the digits of a number in base 8 is divisible by 7 then the original number is also divisible by 7.

Problem 14.
(a)
Based on the results in Problem (13), state a rule for a hexadecimal number to be divisible by 15. No proof necessary.
(b)
Using the rule, is $\mbox{B13A9E4CA}_{16}$ divisble by 15? Show your work.
(c)
Using the rule, is $\mbox{8DB9FC5A2}_{16}$ divisble by 15? Show your work.
(d)
Is the sum of the two values in Parts (b) and (c) divisble by $15$? Why?



Steve Scolnik 2003-09-10