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1




1. , .

1.1. 1011012 :

5 4 3 2 1 0

1011012 = 1´25 + 0´24 + 1´23 +1´22 + 0´21 +1´20 = 32+0+8+4+0+1=4510.

:

1.) 45:2 = 22 (1);

2.) 22:2 = 11 (0);

3.) 11:2 = 5 (1);

4.) 5:2 = 2 (1);

5.) 2:2 = 1 (0).

: 4510= 1011012. .

: 1011012 = 4510.

1.2. 23128 .

3 2 1 0

23128 = 2 ´ 83 +3 ´ 82 +1 ´ 81 +2 ´ 80 = 1024+192+8+2=122610.

:

1.) 1226:8 = 153 (2);

2.) 153:8 = 19 (1);

3.) 19:8 = 2 (3);

 

: 122610= 23128. .

: 23128. = 122610.

 

1.3. 1dc16 .

2 1 0

1dc16 = 1 ´ 162 + 13 ´ 161 +12 ´ 160 = 256+208+12 = 47610.

:

1.) 476:16 = 29 (12);

2.) 29:16 = 1 (13).

 

: 47610= 1dc16. .

: 1dc16 = 47610.

 

5.2. 2

 

2. , .

2.1. 89110 :

 

1) 891:2 = 445 (1), 445 >= 2;

2) 445:2 = 111 (0), 111 >= 2;

3) 111:2 = 55 (1), 55 >= 2;

4) 55:2 = 27 (1), 27 >= 2;

5) 27:2 = 13 (1), 13 >= 2;

6) 13:2 = 6 (1), 6 >= 2;

7) 6:2 = 3 (0), 3 >= 2;

8) 3:2 = 1 (1), 1 < 2 .

: 98110 = 11011110112.

:

9 8 7 6 5 4 3 2 1 0

11011110112 =1´29+1´28+0´27 +1´26 +1´25+1´24+1´23+0´22+1´21+1´20 =

= 512 + 256 + 0 + 64 + 32 + 16 + 8 + 0 + 2 + 1 = 98110..

.

: 89110 = 11011110112.

 

2.2. 891 :

 

1) 891:8 = 111 (3), 111 >= 8;

2) 111:8 = 13 (7), 13 >= 8;

3) 13:8 = 1 (5), 1 < 8 .

: 89110 = 51738

:

3 2 1 0

15738 = 1 ´ 83 + 5 ´ 82 + 7 ´ 81 + 3 ´ 80 = 512 +320 + 56 + 3 = 89110.

.

: 89110 = 15738.

2.3. 89110 :

1) 891:16 = 55 (11), 55 >= 16;

2) 55:16 = 3 (7), 3 < 16 .

: 89110 = 37b16

:

2 1 0

37b16 = 3 ´ 162 + 7 ´ 161 +11 ´ 160 = 768 + 112 + 11 = 89110.

.

: 89110 = 37b16.

1. 17.97 .

1.1. :

1) 17: 2 = 8 (1), 8 >= 2;

2) 8: 2 = 4 (0), 4 >= 2;

3) 4: 2 = 2 (0), 2 >= 2;

4) 2: 2 = 1 (0), 1< 2 .

, 1710 = 100012

1.2. :

1) 0.97 ´ 2 = 1.94 (1);

2) 0.94 ´ 2 = 1.88 (1);

3) 0.88 ´ 2 = 1.76 (1);

4) 0.76 ´ 2 = 1.52 (1);

5) 0.52 ´ 2 = 1.04 (1).

, 0.9710 = 0.111112

, 17.9710 = 10001.111112

2. 17.97 .

2.1. :

1) 17: 8 = 2 (1), 2 < 8 .

, 1710 = 218

2.2. :

1) 0.97 ´ 8 = 7.76 (7);

2) 0.76 ´ 8 = 6.08 (6);

3) 0.08 ´ 8 = 0.64 (0);

, 0.9710 = 0.7608

, 17.9710 = 21.7608

3. 17.97 .

3.1. :

1) 17: 16 = 1 (1), 1 < 16 .

, 1710 = 1116

3.2. :

1) 0.97 ´ 16 = 15.52 (15);

2) 0.52 ´ 16 = 8.32 (8);

, 0.9710 = f816

, 17.9710 = 11.f816

4. 1001.11111 :

4 3 2 1 0-1-2-34-5

10001.11111 2 = 1 ´ 24 + 0 ´ 23 + 0 ´ 22 + 0 ´ 21 +1 ´ 20 +1 ´ 2-1 +1 ´ 2-2 + 1 ´2-3 + 1 ´ 2-4 + 1 ´ 2-5 = 16+0+0+0+1+0.5+0.25+0.125+0.0625+0.03125 = =17.9687510.

: 10001.111112 = 17.9687510,

: 17,97 ≠ 17,96875

5. e:

6. 21.760 .

1 0-1-2-3

21.7608 = 2 ´ 81 + 1´ 80 + 6 ´ 8-2 + 0.8-3 = 16 + 1 + 0.875 + 0.09375 + 0 = 17.9687510.

: 21.7608 = 17.9687510

: 17.97 ≠ 17.96875

7. e:

8. 11.f8 :

 

1 0 -1-2

11.f816 = 1 ´ 161 + 1 ´ 160 + 15 ´ 16 1 + 8 ´16-2 = 16 + 1 + 0.9375 + 0.03125 = 17.9687510

: 11.f851e16 = 17.9687510

: 17.97 ≠ 17.96875

9. e:

3.

 

1. 91 .

1.1. 91 :

1) 91:2=45(1), 45 >= 2;

2) 45:2=22(1), 22 >= 2;

3) 22:2=11(0), 11 >= 2;

4) 11:2=5(1), 5 >= 2;

5) 2:2=1(1), 2 >= 2;

6) 2:2=1(0), 1 < 2-

, 9110 = 10110112.

: 1011011 :

160514130211102 = 1 * 26 + 0 * 25 + 1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 64 + 16 + + 8 + 2 + 1 = 9110.

, 10110112 = 9110.

1.2. 10110112 , :

10110112 =00000000010110112.

, 91, :

 

                               
                               

 

 

2. 91 .

2.1. :

1) 91:2=45(1), 45>=2;

2) 45:2=22(1), 22>=2;

3) 22:2=11(0), 11>=2;

4) 11:2=5(1), 5>=2;

5) 5:2=2(1), 2>=2;

6) 2:2=1(0), 1>2-

, 9110 = 10110112 .

2.2. 1011011 :

10110112 =00000000010110112 .

2.3. 00000000010110110, , :

0000000001011011→ 1111111110100100

2.4 1111111110100100 ,

+

0000000000000001

, -91 1111111110100101:

 

                               
                               

 

3. 11101101 .

11101101

17161504131201102 = 1*27 + 1*26 + 1*25 + 0*24 + 1 * 23 + 1*22 + 0*21+1*20 = 128 + 64+ + 32 + 0 + 8 + 4 + 0 + 1 = 23710

, 111011012 23710.

: 237 :

1) 237: 2 = 118 (1), 118 >=2;

2) 118: 2 = 59 (0), 59 >=2;

3) 59: 2 = 29 (1), 29 >=2;

4) 29: 2 = 14 (1), 14 >=2;

5) 14: 2 = 7 (0), 7 >=2;

6) 7: 2 = 3 (1), 3 >=2;

7) 3: 2 = 1 (1), 1<2- .

, 23710 = 111011012.

4. 11101101

4.1. 11101101: N = 00010010

4.2. ,

+

00000001

, :

N2 = 0010011 = 10011.

4.3 :

N = 10011 = N10 = 1*24 + 0*23 + 0*22 + 1*21 + 1*20 =16 + 0 + 0 + 2 + 1 = 1910

N10 = 1910

4.4 :

N10 = -1910

5. 43.13

5.1 43.13

5.1.1 :

1) 43: 2 = 21 (1), 21 ≥ 2

2) 21: 2 = 10 (1), 10 ≥ 2

3) 10: 2 = 5 (0), 5 ≥ 2

4) 5: 2 = 2 (1), 2 ≥ 2

5) 2: 2 = 1 (0), 1 ≤ 2

, 4310 = 1010112

5.1.2 . m = 24 n, m , n

m = 24 5 = 19:

1) 0.13 ´ 2 = 0.26 à 0;

2) 0.26 ´ 2 = 0.52 à 0;

3) 0.52 ´ 2 = 1.04 à 1;

4) 0.04 ´ 2 = 0.08 à 0;

5) 0.08 ´ 2 = 0.16 à 0;

6) 0.16 ´ 2 = 0.32 à 0;

7) 0.32 ´ 2 = 0.64 à 0;

8) 0.64 ´ 2 = 1.28 à 1;

9) 0.28 ´ 2 = 0.56 à 0;

10) 0.56 ´ 2 = 1.12 à 1;

11) 0.12 ´ 2 = 0.24 à 0;

12) 0.24 ´ 2 = 0.48 à 0;

13) 0.48 ´ 2 = 0.96 à 0;

14) 0.96 ´ 2 = 1.92 à 1;

15) 0.92 ´ 2 = 1.84 à 1;

16) 0.84 ´ 2 = 1.68 à 1;

17) 0.68 ´ 2 = 1.36 à 1;

18) 0.36 ´ 2 = 0.72 à 0

19) 0.72 ´ 2 = 1.44 à 1.

, 0.1310 = 0.00100001010001111012

, 43.1310 = 101011.00100001010001111012.

: 101011.0010000101000111101 :

150413021110.0-10-21-30-40-50-60-71-80-91-100-110-120-131-141-151-161-170-181-192 = 1 * 25 + 0 ´ 24 + 1 ´ 23 + 0 ´ 22 + 1 ´ 21 + 1 ´ 20 + 0 ´ 2-1 + 0 ´ 2-2 + 1 ´ 2-3 + 0 ´ 2-4 + 0 ´ 2-5 + 0 ´ 2-6 + 0 ´ 2-7 + 1 ´ 2-8 + 0 ´ 2-9 +1 ´ 2-10 + 0 ´ 2-11 + 0 ´ 2-12 + 0 ´ 2-13 + 1 ´ 2-14 + 1 ´ 2-15 + 1 ´ 2-16 + 1 ´ 2-17 + 0 ´ 2-18 + 1 ´ 2-19 = 32 + 8 + 2 + 1 + 0.125 + 0.00390625 + 0.0009765625 + 0.00006103515625 + 0.000030517578125 + 0.0000152587890625 + 0.00000762939453125 + 0.0000019073486328125 + ≈ 43.13.

, 101011.00100001010001111012 ≈ 43.1310.

5.2. . , :

 

101011.0010000101000111101

+

0.0000000000000000001

101011.0010000101000111110

5.3. . :

101011.0010000101000111112

5.4. , :

101011.0010000101000111112 = 1.010110010000101000111112 * 2510

5.5. :

1.010110010000101000111112 à 0.010110010000101000111112

5.6. :

510 + 12710 = 13210 = 100001002.

5.7. : 0.

5.8. 43.13 :

 

1 2 3 4
                                                               
                                                               
            f
                                                                   

 


 





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