1

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

N = 6

2

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0

i

N = 6

3

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 1

i v

N = 6

4

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 1

i v

true

i <= N

N = 6

5

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 10 1

i v

true

i <= N

N = 6

6

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 10 1

i v

1

true

i <= N

N = 6

7

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 10 1

i v

1 2

true

i <= N

N = 6

8

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 10 1

i v

1 2

true

i <= N

true

N = 6

9

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 2

0 1

i v

1 2

true

i <= N

true

N = 6

10

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 2

0 1

i v

1 2

2

true

i <= N

true

N = 6

11

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 2

0 1

i v

1 2

2 4

true

i <= N

true

N = 6

12

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 2

0 1

i v

1 2

2 4

true

i <= N

true

true

N = 6

13

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 4

0 1

i v

1 2

2 4

true

i <= N

true

true

N = 6

14

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 4

0 1

i v

1 2

2 4

3

true

i <= N

true

true

N = 6

15

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 4

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

N = 6

16

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 4

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

N = 6

17

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 8

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

N = 6

18

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 8

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4

N = 6

19

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 8

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

N = 6

20

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 8

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16 true

N = 6

21

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 16

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16 true

N = 6

22

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 16

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5

true

N = 6

23

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 16

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

true

N = 6

24

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 16

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

true

true

N = 6

25

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 32

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

true

true

N = 6

26

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 32

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6

true

true

N = 6

27

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 32

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

true

true

N = 6

28

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 32

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

true

true

true

N = 6

29

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 326 64

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

true

true

true

N = 6

30

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 326 64

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

7

true

true

true

N = 6

31

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 326 64

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

7 128

true

true

true

N = 6

32

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 326 64

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

7 128

true

true

true

false

N = 6

33

Powers of Two: Trace

Ex. Print powers of 2 that are 2N. Increment i from 0 to N. Double v each time.

int i = 0;int v = 1;while (i <= N) { System.out.println(i + " " + v); i = i + 1; v = 2 * v;}

0 11 22 43 84 165 326 64

0 1

i v

1 2

2 4

3 8

true

i <= N

true

true

true

4 16

5 32

6 64

7 128

true

true

true

false

N = 6