Question

Name: 9. Work one of the following problems. You may work the second problem for extra credit if you have time. Problem 1: (a) Convert the decimal number 201 to an octal number. (b) Convert the hexadecimal numeral C1E$_{16}$ to a binary numeral. (b) Trace this algorithm when n = 19. (Trace = "complete a table that identifies each value of each variable as the algorithm is executed, make sure you record the output of the algorithm) procedure base 2 expansion (n: positive integer) q = n k = 0 while q \neq 0 a$_k$ = q mod 2 q = q div 2 k = k + 1 return ($a_k$, ..., $a_1$, $a_0$) Problem 2: Use induction to prove that if n is an integer \geq 2 and G is a tree with n vertices then G has n-1 edges.

          Name:
9. Work one of the following problems. You may work the second problem for extra credit if
you have time.
Problem 1:
(a) Convert the decimal number 201 to an octal number.
(b) Convert the hexadecimal numeral C1E$_{16}$ to a binary numeral.
(b) Trace this algorithm when n = 19. (Trace = "complete a table that identifies each value
of each variable as the algorithm is executed, make sure you record the output of the
algorithm)
procedure base 2 expansion (n:
positive integer)
q = n
k = 0
while q \neq 0
a$_k$ = q mod 2
q = q div 2
k = k + 1
return ($a_k$, ..., $a_1$, $a_0$)
Problem 2: Use induction to prove that if n is an integer \geq 2 and G is a tree with n vertices then
G has n-1 edges.

Name:
9. Work one of the following problems. You may work the second problem for extra credit if
you have time.
Problem 1:
(a) Convert the decimal number 201 to an octal number.
(b) Convert the hexadecimal numeral C1E16 to a binary numeral.
(b) Trace this algorithm when n = 19. (Trace = "complete a table that identifies each value
of each variable as the algorithm is executed, make sure you record the output of the
algorithm)
procedure base 2 expansion (n:
positive integer)
q = n
k = 0
while q ≠0
ak = q mod 2
q = q div 2
k = k + 1
return (ak, ..., a1, a0)
Problem 2: Use induction to prove that if n is an integer ≥2 and G is a tree with n vertices then
G has n-1 edges.

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