CSci 107 Practice Problems - Bowdoin College
More practice problems
1. Suppose you have two 2-bit binary numbers, x1x2 and y1y2. Each one can be 00, 01, 10, or 11, representing the decimal values 0, 1, 2, and 3 respectively. Design a truth table or a logic circuit that determines whether or not the binary numbers x1x2 and y1y2 are equal.
2. Write a recursive method exp that raises a positive (> 0) integer to a non-negative (>= 0) power; i.e. exp(3,2) should return 9. To do this, it helps to think about exponentiation recursively. If we want to raise m to the n power, we can think as follows:
m n = 1 if n = 0
m n = m x m n-1 if n>0
Suggested test inputs (correct answer after arrow):
exp (3,2) ( 9
exp(83,0) ( 1
exp(124, 1) ( 124
exp(1,124) ( 1
exp(5,4) ( 625
exp(10,3) ( 1000
3. Write a recursive method fib that computes the nth Fibonacci numbers (fib(n)). The Fibonacci numbers are defined as follows:
fib(0) = 0
fib(1) = 1
fib(n) = fib(n-1) + fib(n-2) if n>1
Suggested test inputs (correct answer after arrow):
fib(0) ( 0
fib(1) ( 1
fib(2) ( 1
fib(3) ( 2
fib(4) ( 3
fib(10) ( 55
fib(20) ( 6765
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