Complete the cross word puzzle.
(1) Left to Right
Example:
(a) 5 in base 2 (3 sq)
(b) 7 in base 2 (3)
(d) 12 in base 2 (4)
(e) 8 in base 2 (4)
(f) 4 in base 2 (3)
(i) 13 in base 2 (4)
(2) Down
(a) 15 in base 2 (4 sq)
(c) 10 in base 2 (4)
(e) 14 in base 2 (4)
(f) 2 in base 2 (2)
(g) 3 in vase 2 (2)
(h) 11 in base 2 (4)
(i) 6 in base 2 (3)
a1
0
g1
b
e
d
e
h
i
f
Complete the cross word puzzle.
(1) Left to Right
Example:
(a) 5 in base 2 (3 sq)
(b) 7 in base 2 (3)
(d) 12 in base 2 (4)
(e) 8 in base 2 (4)
(f) 4 in base 2 (3)
(i) 13 in base 2 (4)
(2) Down
(a) 15 in base 2 (4 sq)
(c) 10 in base 2 (4)
(e) 14 in base 2 (4)
(f) 2 in base 2 (2)
(g) 3 in vase 2 (2)
(h) 11 in base 2 (4)
(i) 6 in base 2 (3)
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g1 |
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e |
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(1) 1(2) = 1 × 20 = 1 × 1 = 1
∴ 1(2) = 1
(2) 11(2)
21
20
1
1
∴11(2) = 1 × 21 + 1 × 20 = 1 × 2 + 1 × 1 = 2 + 1 = 3
∴ 11(2) = 3
(3) 101(2)
22
21
20
1
0
1
Therefore,
101(2) =1×22 +0×21 + 1×20
= 1 × 4 + 0 × 2 + 1 ×1
= 4 + 0 + 1
= 5
∴ 101(2) = 5
(4) 100(2)
22
21
20
1
0
0
∴100(2) =1×22 +0×21 + 0×20 = 1 × 4 + 0 × 2 + 0 ×1 = 4 + 0 + 0 = 4
∴ 100(2) = 4
(5) 111(2)
22
21
20
1
1
1
111(2) = 1 × 22 + 1 × 21 + 1 × 20 = 1 × 4 + 1 × 2 + 1 ×1 = 4 + 2 + 1 = 7
∴ 111(2) = 7
(6) 1001(2)
23
22
21
20
1
0
0
1
1001(2) =1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 8 + 0 + 0 + 1 = 9
∴ 1001(2) = 9
(7) 1110(2)
23
22
21
20
1
1
1
0
1110(2) =1 × 23 + 1 × 22 + 1 × 21 + 0 × 20
= 1 × 8 + 1 × 4 + 1 × 2 + 0 × 1
= 8 + 4 + 2 + 0
= 14
∴ 1110(2) = 14
(8) 1010(2)
23
22
21
20
1
0
1
0
1010(2) = 1 × 23+ 0 × 22 + 1 × 21 + 0 × 20
= 1 × 8 + 0 × 4 + 1 × 2 + 0 ×1
= 8 + 0 + 2 + 0
= 10
∴ 1010(2) = 10
(9) 1111(2)
23
22
21
20
1
1
1
1
1111(2) = 1× 23+ 1 × 22 +1 × 21 + 1 × 20
= 1 × 8 + 1 × 4 + 1 × 2 + 1 ×1
= 8 + 4 + 2 + 1
= 15
∴ 1111(2) = 15
(10) 11001(2)
24
23
22
21
20
1
1
0
0
1
11001(2) = 1× 24 + 1 × 23+ 0 × 22 + 0 × 21 + 1 × 20
= 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 16 + 8 + 0 + 0 + 1
= 25
∴ 11001(2) = 25
(1)
(b) 7 = (1 × 22) + (1 × 21) + (1 × 20) = 111(2)
(d) 12 = (1 × 23) + (1 × 22) + (0 × 21) + (0 × 20) = 1100(2)
(e) 8 = (1 × 23) + (0 × 22) + (0 × 21) + (0 × 20) = 1000(2)
(f) 4 = (1 × 22) + (0 × 21) + (0 × 20) = 100(2)
(i) 13 = (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) = 1101(2)
(2)
(a) 15 = (1 × 23) + (1 × 22) + (1 × 21) + (1 × 20) = 1111(2)
(c) 10 = (1 × 23) + (0 × 22) + (1 × 21) + (0 × 20) = 1010(2)
(e) 14 = (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20) = 1110(2)
(f) 2 = (1 × 21) + (0 × 20) = 10(2)
(g) 3 = (1 × 21) + (1 × 20) = 11(2)
(h) 11 = (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20) = 1011(2)
(i) 6 = 110(2)
Therefore, the solution of the puzzle is
a
1
0
g
1
b
1
1
c
1
1
1
d
1
1
0
0
1
1
1
e
1
0
0
0
0
1
h
1
1
i
1
1
0
1
f
1
0
0
1
1
0
0
1
(1) 1(2) = 1 × 20 = 1 × 1 = 1
∴ 1(2) = 1
(2) 11(2)
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21 |
20 |
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1 |
1 |
∴11(2) = 1 × 21 + 1 × 20 = 1 × 2 + 1 × 1 = 2 + 1 = 3
∴ 11(2) = 3
(3) 101(2)
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22 |
21 |
20 |
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1 |
0 |
1 |
Therefore,
101(2) =1×22 +0×21 + 1×20
= 1 × 4 + 0 × 2 + 1 ×1
= 4 + 0 + 1
= 5
∴ 101(2) = 5
(4) 100(2)
|
22 |
21 |
20 |
|
1 |
0 |
0 |
∴100(2) =1×22 +0×21 + 0×20 = 1 × 4 + 0 × 2 + 0 ×1 = 4 + 0 + 0 = 4
∴ 100(2) = 4
(5) 111(2)
|
22 |
21 |
20 |
|
1 |
1 |
1 |
111(2) = 1 × 22 + 1 × 21 + 1 × 20 = 1 × 4 + 1 × 2 + 1 ×1 = 4 + 2 + 1 = 7
∴ 111(2) = 7
(6) 1001(2)
|
23 |
22 |
21 |
20 |
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1 |
0 |
0 |
1 |
1001(2) =1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 8 + 0 + 0 + 1 = 9
∴ 1001(2) = 9
(7) 1110(2)
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23 |
22 |
21 |
20 |
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1 |
1 |
1 |
0 |
1110(2) =1 × 23 + 1 × 22 + 1 × 21 + 0 × 20
= 1 × 8 + 1 × 4 + 1 × 2 + 0 × 1
= 8 + 4 + 2 + 0
= 14
∴ 1110(2) = 14
(8) 1010(2)
|
23 |
22 |
21 |
20 |
|
1 |
0 |
1 |
0 |
1010(2) = 1 × 23+ 0 × 22 + 1 × 21 + 0 × 20
= 1 × 8 + 0 × 4 + 1 × 2 + 0 ×1
= 8 + 0 + 2 + 0
= 10
∴ 1010(2) = 10
(9) 1111(2)
|
23 |
22 |
21 |
20 |
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1 |
1 |
1 |
1 |
1111(2) = 1× 23+ 1 × 22 +1 × 21 + 1 × 20
= 1 × 8 + 1 × 4 + 1 × 2 + 1 ×1
= 8 + 4 + 2 + 1
= 15
∴ 1111(2) = 15
(10) 11001(2)
|
24 |
23 |
22 |
21 |
20 |
|
1 |
1 |
0 |
0 |
1 |
11001(2) = 1× 24 + 1 × 23+ 0 × 22 + 0 × 21 + 1 × 20
= 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 16 + 8 + 0 + 0 + 1
= 25
∴ 11001(2) = 25
(1)
(b) 7 = (1 × 22) + (1 × 21) + (1 × 20) = 111(2)
(d) 12 = (1 × 23) + (1 × 22) + (0 × 21) + (0 × 20) = 1100(2)
(e) 8 = (1 × 23) + (0 × 22) + (0 × 21) + (0 × 20) = 1000(2)
(f) 4 = (1 × 22) + (0 × 21) + (0 × 20) = 100(2)
(i) 13 = (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20) = 1101(2)
(2)
(a) 15 = (1 × 23) + (1 × 22) + (1 × 21) + (1 × 20) = 1111(2)
(c) 10 = (1 × 23) + (0 × 22) + (1 × 21) + (0 × 20) = 1010(2)
(e) 14 = (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20) = 1110(2)
(f) 2 = (1 × 21) + (0 × 20) = 10(2)
(g) 3 = (1 × 21) + (1 × 20) = 11(2)
(h) 11 = (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20) = 1011(2)
(i) 6 = 110(2)
Therefore, the solution of the puzzle is
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a 1 |
0 |
g 1 |
b 1 |
1 |
c 1 |
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1 |
1 |
d 1 |
1 |
0 |
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1 |
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e 1 |
0 |
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0 |
0 |
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1 |
h 1 |
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1 |
i 1 |
1 |
0 |
1 |
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f 1 |
0 |
0 |
1 |
1 |
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0 |
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1 |
