Homework 1
Due at the start of class Wednesday, September 17, 2003.
Show your work on Problems 1 to 12.
- Problem 1.
- Convert
to a base 10 number.
- Problem 2.
- Convert
to a base 7 number.
- Problem 3.
- Convert
to a base 4 number.
- Problem 4.
- Convert
to octal.
- Problem 5.
- Convert
to hexadecimal.
- Problem 6.
- Convert
to hexadecimal.
- Problem 7.
- Add
.
- Problem 8.
- Subtract
.
- Problem 9.
- Convert
to decimal notation.
- Problem 10.
- Convert
to decimal notation.
- Problem 11.
- Convert
to binary notation
(with a binary point).
- Problem 12.
- Convert
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
divisble by 15? Show your work.
- (c)
- Using the rule, is
divisble by 15? Show your work.
- (d)
- Is the sum of the two values in Parts (b) and (c) divisble by
? Why?
Steve Scolnik
2003-09-10