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Tracing & Understanding Algorithms1. What does the following algorithm do?

Divide an integer by 2.

2. TRA!"# A$#%R!T!'

n(m)*

1. while x=/= 0 repeat the following 

(num=1) (result=””)

2. appendLeft num mod 2 to result 

 (num=6)(result=”0”)

3. set num to num div 2

(num=3) (result=”0”) 4. end while loop

(num=3) (result=”0”)

 

(loop #2) num=3

1. while x=/= 0 repeat the following 

(num=3)(result=””)

2. appendLeft num mod 2 to result 

  (num=3)(result=”1”)3. set num to num div 2

 (num=1) (result=”1”)

 4. end while loop

(num=1) (result=”1”)

(loop # 3) num=1

1. while x=/= 0 repeat the following 

(num=1)(result=””)2. appendLeft num mod 2 to result 

(num=1) (result=”1”)

3. set num to num div 2

(num=0) (result=”1”)

 4. end while loop

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(num=0, so no more loops)(result=”1”)

Num=13

1. while x=/= 0 repeat the following 

(num=13) (result=””)

2. appendLeft num mod 2 to result 

(num=13) (result=”1”)

3. set num to num div 2

(num=6) (result=”1”)

 4. end while loop

(num=6) (result=”1”)

(loop 2) num=6

1. while x=/= 0 repeat the following 

(num=6) (result=””)

2. appendLeft num mod 2 to result 

(num=6) (result=”0”)

3. set num to num div 2

 (num=3) (result=”0”)

 4. end while loop

(num=3) (result=”0”)

  (loop 3) num=3

1. while x=/= 0 repeat the following 

  (num=3) (result=””)

2. appendLeft num mod 2 to result 

(num=3) (result=”1”)

3. set num to num div 2

(num=1) (result=”1”)

 4. end while loop(num=1) (result=”1”)

  (loop 4) num=1

1. while x=/= 0 repeat the following 

(num=1) (result=””)

2. appendLeft num mod 2 to result 

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(num=1) (result=”1”)

3. set num to num div 2

(num=0) (result=”1”)

 4. end while loop

(num=0, so no more loops) (result=”1”)

Num=163

1. while x=/= 0 repeat the following 

(num=163) (result=””)

2. appendLeft num mod 2 to result 

(num=163) (result=”1”)

3. set num to num div 2

(num=!1) (result=”1”)

 4. end while loop

(num=!1) (result=”1”)

(loop 2) num=!1

1. while x=/= 0 repeat the following 

(num=!1) (result=””)

2. appendLeft num mod 2 to result 

(num=!1) (result=”1”)

3. set num to num div 2

(num=40) (result=”1”)

 4. end while loop

(num=40) (result=”1”)

(loop 3) num=40

1. while x=/= 0 repeat the following 

(num=40) (result=””)

2. appendLeft num mod 2 to result 

(num=40) (result=”0”)3. set num to num div 2

(num=20) (result=”0”)

 4. end while loop

(num=20) (result=”0”)

(loop 4) num=20

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1. while x=/= 0 repeat the following 

(num=20) (result=””)

2. appendLeft num mod 2 to result 

(num=20) (result=”0”)

3. set num to num div 2

(num=10) (result=”0”)

 4. end while loop

(num=10) (result=”0”)

(loop ") num=10

1. while x=/= 0 repeat the following 

(num=10) (result=””)

2. appendLeft num mod 2 to result 

(num=10) (result=”0”)

3. set num to num div 2

(num=") (result=”0”)

 4. end while loop

(num=") (result=”0”)

(loop 6) num="

1. while x=/= 0 repeat the following 

(num=") (result=””)

2. appendLeft num mod 2 to result 

(num=") (result=”1”)

3. set num to num div 2

(num=2) (result=”1”)

 4. end while loop

(num=2) (result=”1”)

(loop #) num=2

1. while x=/= 0repeat the following 

(num=2) (result=””)

2. appendLeft num mod 2 to result 

(num=2) (result=”0”)

3. set num to num div 2

(num=1) (result=”0”)

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 4. end while loop

(num=1) (result=”0”)

(loop !) num=1

1. while x=/= 0 repeat the following 

(num=1) (result=””)

2. appendLeft num mod 2 to result 

(num=1) (result=”1”)

3. set num to num div 2

(num=0) (result=”1”)

 4. end while loop

(num=0, so no more loops) (result=”1”)