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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