Esercizi Informatica - conversione logica, diagrammi di flusso

AE12₁₆ IN BINARIO

A = 1010

1. 5 2 0
2. 2 1 0
3. 1 0 1
4. 0

E = 14

1. 7 2 1
2. 3 2 1
3. 1 2 1
4. 0

10101110010₂

AE12₁₆ IN DECIMALE

10 * 16³ + 14 * 16² + 1 * 16¹ + 2 * 16⁰ = 44562₁₀

44562₁₀ IN ESADECIMALE

1. 44562 \ 16 q = 2
2. 2785 \ 16 q = 1
3. 174 \ 16 q = 14
4. 10 \ 16 q = 10
5. 0

10 14 1 2

A E 1 2

AE12₁₆ IN BINARIO

A = 1010

1. 5 2 0
2. 2 1 0
3. 2 1 0
4. 1 0 1
5. 0

E = 14

1. 7 2 0
2. 3 2 1
3. 1 2 1
4. 0

101011100010₂

AE12₁₆ IN DECIMALE

10.16³ + 14.16² + 1.16¹ + 2.16⁰ = 44562₁₀

44562₁₀ IN ESADEMALE

1. 44562 16 x = 2
2. 2785 16 r = 1
3. 174 16 r = 14
4. 10 16 r = 10
5. 0

10 14 1 2

A E 1 2

COMPLEMENTO A 2

N = 26 = NUM. DA RAPP.

m = n. bit = ⌈log₂(26 + 1)⌉ = 5

2^m = 32

2^m - 26 = 32 - 26 = 6₁₀

6₁₀ →

• 6 | 2 - 0
• 3 | 2 - 1
• 1 | 2 - 1
• 0

= 110₂ = -26_(2^m-N)

EXTRA

+26_(2^m-N) = 001 + 1 = 010₂

m = 6

N = -74

2⁶ - 74 = -10₁₀

• 10 | 2 0
• 5 | 2 1
• 2 | 2 0
• 1 | 2 1
• 0

11010 = 10₁₀ = -74_(2^m-N)

0.786₁₀ IN BINARIO

• 0.786 | 2 → 1
• 0.572 | 2 → 1
• 0.144 | 2 → 0
• 0.288 | 2 → 0
• 0.576 | 2 → 1

0.11001

0.11001 IN DECIMALE

1 · 2^-1 + 1 · 2^-2 + 1 · 2^-5 = 0.5 + 0.25 + 0.03125 = 0.786

-24,206 in virgola mobile

24,206₁₀

• 24 ÷ 2 = 0
• 12 ÷ 2 = 0
• 6 ÷ 2 = 0
• 3 ÷ 2 = 1
• 1 ÷ 2 = 1

0,206 ÷ 2 = 0

0,412 ÷ 2 = 0

0,824 ÷ 2 = 1

1,000001 • 2⁴ = 1,1000001 • 2⁴

4 + 127 = 131

• 131 ÷ 2 = 1
• 65 ÷ 2 = 1
• 32 ÷ 2 = 0
• 16 ÷ 2 = 0
• 8 ÷ 2 = 0
• 4 ÷ 2 = 0
• 2 ÷ 2 = 0
• 1 ÷ 2 = 1

e = 10000011₂ = 2⁰ + 2¹ + 2⁷ = 131

131 - 127 = 4

(-1)^s • 2^e • (1,m)

m = 1 • 2^-1 + 1 • 2^-7 = 0,5078125

(-1)¹ • 2⁴ • (1,5078125) = -24,206

2476₈ IN BINARIO

2 1 2₈

1 2 0₈

4 2 0₈

3 2 1₈

7 2 1₈

3 2 1₈

6 2 0₈

3 2 1₈

0 1₈

1 1₈

2 1₈

2 1₈

4 1₈

0₈

1 0 1 2₈

1 1 2 0₈

1 2 0₈

1 1 1₈

0₈

0₈

2

0 1 0 1 0 0 1 1 1 1 0

0 1 0 1 0 0 1 1 1 1 0₂ IN ESADECIMALE

0 1 0 1₂ = 1 . 2² + 1 . 2⁰ = 5₁₆

0 0 1 1₂ = 1 . 2¹ + 1 . 2⁰ = 3₁₆

1 1 1 0₂ = 1 . 2³ + 1 . 2² + 1 . 2¹ = 8 + 4 + 2 = 14 = E₁₆

53E₁₆ IN DECIMALE

5 . 16² + 3 . 16¹ + 14 . 16⁰ = 1342₁₀

1342₁₀ IN OTTALE

1 3 4 2₈ r = 6

1 6 7₈ r = 7

2 0₈ r = 4

2₈ r = 2

0

2 4 7 6 8

2031₁₀ in binario

2031 | 2 | 1

1015 | 2 | 1

507 | 2 | 1

253 | 2 | 1

126 | 2 | 0

63 | 2 | 1

31 | 2 | 1

15 | 2 | 1

7 | 2 | 1

3 | 2 | 1

1 | 0

01111011111₂ in ottale

011₂ = 1·2¹ + 1·2⁰ = 3₈

111₂ = 1·2² + 1·2¹ + 1·2⁰ = 7₈

102₂ = 1·2² + 1·2⁰ = 5₈

111₂ = 7₈

3757₈ in decimale

3·8³ + 7·8² + 5·8¹ + 7·8⁰ = 2031₁₀

2031₁₀ in esadecimale

2031 | 16 | n = 15

126 | 16 | n = 14

7 | 16 | n = 7

0

7EF₁₆

7EF₁₆ in decimale

7·16² + 14·16¹ + 15 = 2031₁₀

86,49

186,49

86 | 2 | 0

43 | 2 | 1

21 | 2 | 1

10 | 2 | 0

5 | 2 | 1

2 | 2 | 0

1 | 2 | 1

0,49 : 2 | 0

0,98 : 2 | 0

0,96 : 2 | 1

0,92 :...

0,1 : 2

1,10001010,110₂

1,0101101

0,0101₂

127 + 6 = 133₁₀

133 | 2 | 1

66 | 2 | 0

33 | 2 | 1

16 | 2 | 0

8 | 2 | 0

4 | 2 | 0

2 | 2 | 1

1 | 2 | 1

1 10000101 010110110000000000000000

10000101 = 1 . 2⁷ + 1 . 2² + 1 . 2⁰

= 133

e = 133 - 127 = 6

m = 1 . 2^-2 + 1 . 2^-4 + 1 . 2^-5 + 1 . 2^-7 + 1 . 2^-8

m = 0,3

(1)⁵ . 2⁰ (1,m) = -86,49

Esercizi Informatica

150₁₀ in Binario

• 150 | 0
• 75 | 1
• 37 | 1
• 18 | 0
• 9 | 1
• 4 | 0
• 2 | 0
• 1 | 1

10010110

10010110₂ in Decimale

1∙2⁷ + 0∙2⁶ + 0∙2⁵ + 1∙2⁴ + 0∙2³ + 1∙2² + 1∙2¹ + 0∙2⁰ = 150

150₁₀ in Esadecimale

• 150 | 6
• 9 | 9
• 0

96₁₆ in Decimale

9 ∙ 16¹ + 6 ∙ 16⁰ = 150₁₀

96₁₆ in Binario

• 9 | 1
• 4 | 0
• 2 | 0
• 1 | 1
• 0

• 6 | 0
• 3 | 1
• 1 | 1
• 0

10010110

10010110₂ in Esadecimale

1001 = 1∙2³ + 0∙2² + 0∙2¹ + 1∙2⁰ = 9

0110 = 0∙2³ + 1∙2² + 1∙2¹ + 0∙2⁰ = 6

150₁₀ in Ottale

• 150 | 6
• 18 | 2
• 2 | 2
• 0

226₈

226₈ in Decimale

2∙8² + 2∙8¹ + 6∙8⁰ = 150₁₀

226₈ in Binario

• 2 | 1
• 1 | 0
• 2 | 1
• 1 | 0
• 6 | 1
• 3 | 1
• 1 | 1
• 0

010010110

010010110₂ in Ottale

010 = 0∙2² + 1∙2¹ + 0∙2⁰ = 2

010 = 0∙2² + 1∙2¹ + 0∙2⁰ = 2

110 = 1∙2² + 1∙2¹ + 0∙2⁰ = 6

226₈

[ (5==5 AND 6!=5) OR 10