Действия над числами в различных системах счисления
В заданиях 3-5 проверять правильность
вычисления переводом исходных данных и результатов в двоичную систему
счисления. В задании 1д получить пять знаков после запятой в двоичном
представлении.
Таблица 1. Наиболее важные
системы счисления.
|
Двоичная (Основание
2)
|
Восьмеричная
(Основание 8)
|
Десятичная
(Основание 10)
|
Шестнадцатиричная
(Основание 16)
|
|
триады
|
|
тетрады
|
|
0 1
|
0 1 2 3 4 5
6 7
|
000 001 010
011 100 101 110 111
|
0 1 2 3 4 5
6 7 8 9
|
0 1 2 3 4 5
6 7 8 9 A B C D E F
|
0000 0001 0010
0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
|
Перевод целых десятичных чисел в
недесятичную систему
счисления осуществляется последовательным делением десятичного числа на
основание той системы, в которую оно переводится, до тех пор, пока не получится
частное меньшее этого основания. Число в новой системе записывается в виде
остатков деления, начиная с последнего.
Пример.
а) Перевести 18110"8" с.с.
Результат: 18110 = 2658
б) Перевести 62210"16" с.с.
Результат: 62210 = 26E16
Для преобразования в десятичную используют следующую таблицу
степеней основания
Преобразование дробных десятичных чисел:
·
Вначале
переводится целая часть десятичной дроби;
·
Затем дробная
часть десятичной дроби умножается на основание системы счисления;
·
В полученном
произведении выделяется целая часть, которая принимается в качестве значения
первого после запятой разряда числа в системе счисления;
·
Алгоритм
завершается, если дробная часть полученного произведения равна нулю или если
достигнута требуемая точность вычислений. В противном случае вычисления
продолжаются с предыдущего шага.
Правила выполнения арифметических
действий над двоичными числами задаются таблицами двоичных сложения, вычитания и умножения.
|
Таблица
двоичного сложения
|
Таблица
двоичного вычитания
|
Таблица
двоичного умножения
|
|
0+0=0 0+1=1
1+0=1 1+1=10
|
0-0=0 1-0=1
1-1=0 10-1=1
|
00=0 01=0 10=0 11=1
|
Сложение в восьмеричной системе
Сложение в
шестнадцатиричной системе
Умножение в восьмеричной системе
Умножение в шестнадцатеричной системе
1. Перевести данное число из десятичной системы счисления в
двоичную, восьмеричную и шестнадцатеричную системы счисления
а)945(10)=1110110001(2)=1661(8)=3B1(16)
|
945
|
2
|
|
|
|
|
|
|
|
|
|
|
|
944
|
472
|
2
|
|
|
|
|
|
|
|
|
|
|
1
|
472
|
236
|
2
|
|
|
|
|
|
|
|
|
|
0
|
236
|
118
|
2
|
|
|
|
|
|
|
|
|
|
0
|
118
|
59
|
2
|
|
|
|
|
|
|
|
|
|
0
|
58
|
29
|
2
|
|
|
|
|
|
|
|
|
|
|
1
|
28
|
14
|
2
|
|
|
|
|
|
|
|
|
|
1
|
14
|
7
|
2
|
|
|
|
|
|
|
|
|
|
0
|
6
|
3
|
2
|
|
|
|
|
|
|
|
|
|
1
|
2
|
1
|
2
|
|
|
|
|
|
|
|
|
|
1
|
0
|
0
|
|
|
|
|
|
|
|
|
|
|
1
|
0
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
|
|
512
|
256
|
128
|
|
32
|
16
|
|
|
|
1
|
945
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
945,000
|
8,000
|
|
|
|
944,000
|
118,000
|
8,000
|
|
|
1,000
|
112,000
|
14,000
|
8,000
|
|
6,000
|
8,000
|
1,000
|
|
|
6,000
|
1,000
|
|
4096
|
512
|
64
|
8
|
1
|
|
1,000
|
6,000
|
6,000
|
1,000
|
|
945
|
512
|
384
|
48
|
1
|
|
945,000
|
16,000
|
|
|
944,000
|
59,000
|
16,000
|
|
1,000
|
48,000
|
3,000
|
|
11,000
|
|
|
|
|
|
B
|
|
|
3,000
|
11,000
|
1,000
|
|
4096
|
256
|
16
|
1
|
|
3
|
11
|
1
|
|
945
|
768
|
176
|
1
|
б)85 (10)=1010101(2)=125(8)= 55(16)
|
85
|
2
|
|
|
|
|
|
|
|
84
|
42
|
2
|
|
|
|
|
|
|
1
|
42
|
21
|
2
|
|
|
|
|
|
0
|
20
|
10
|
2
|
|
|
|
|
|
1
|
10
|
5
|
2
|
|
|
|
|
|
0
|
4
|
2
|
2
|
|
|
|
|
|
1
|
2
|
1
|
2
|
|
|
|
|
|
0
|
0
|
0
|
|
|
|
|
|
|
1
|
0
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
0
|
1
|
0
|
1
|
0
|
1
|
|
|
|
|
64
|
|
16
|
|
4
|
|
1
|
85
|
|
85,000
|
8,000
|
|
|
|
80,000
|
10,000
|
8,000
|
|
|
5,000
|
8,000
|
1,000
|
|
|
2,000
|
|
|
|
4096
|
512
|
64
|
8
|
1
|
|
|
1,000
|
2,000
|
5,000
|
|
85
|
0
|
64
|
16
|
5
|
|
|
|
|
|
|
|
|
|
85,000
|
16,000
|
|
80,000
|
5,000
|
|
5,000
|
|
|
4096
|
256
|
16
|
1
|
|
|
5
|
5
|
|
85
|
0
|
80
|
5
|
в)444,125 (10)= 110111100,001(2)=674.1(8)=1BC.2(16)
|
444
|
2
|
|
|
|
|
|
|
|
|
|
444
|
222
|
2
|
|
|
|
|
|
|
|
|
0
|
222
|
111
|
2
|
|
|
|
|
|
|
|
0
|
110
|
55
|
2
|
|
|
|
|
|
|
|
1
|
54
|
27
|
2
|
|
|
|
|
|
|
|
1
|
26
|
13
|
2
|
|
|
|
|
|
|
|
1
|
12
|
6
|
2
|
|
|
|
|
|
|
|
1
|
6
|
3
|
2
|
|
|
|
|
|
|
|
0
|
2
|
1
|
2
|
|
|
|
|
|
|
|
1
|
0
|
0
|
|
|
|
|
|
|
|
|
1
|
0
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
|
|
256
|
128
|
|
32
|
16
|
8
|
4
|
|
|
444
|
|
0,125
|
*
|
2
|
=
|
0,250
|
0
|
|
0,250
|
*
|
2
|
=
|
0,500
|
0
|
|
0,500
|
*
|
2
|
=
|
1,000
|
1
|
|
444,000
|
8,000
|
|
|
|
440,000
|
55,000
|
8,000
|
|
|
4,000
|
48,000
|
6,000
|
|
|
7,000
|
|
|
|
4096
|
512
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
|
|
6,000
|
7,000
|
4,000
|
|
1
|
|
|
|
444
|
0
|
384
|
56
|
4
|
|
0,125
|
|
0,125
|
|
|
|
|
|
|
|
|
|
|
|
|
|
444,000
|
16,000
|
|
|
432,000
|
27,000
|
16,000
|
|
12,000
|
16,000
|
1,000
|
|
11,000
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
|
1
|
11
|
12
|
|
2
|
|
444
|
256
|
176
|
12
|
|
0,125
|
г)989,375 (10)= 111 10111 01 ,011(2)=1735.3(8)=3DD.6(16)
|
989
|
2
|
|
|
|
|
|
|
|
|
|
|
988
|
494
|
2
|
|
|
|
|
|
|
|
|
|
1
|
494
|
247
|
2
|
|
|
|
|
|
|
|
|
0
|
246
|
123
|
2
|
|
|
|
|
|
|
|
|
1
|
122
|
61
|
2
|
|
|
|
|
|
|
|
|
1
|
60
|
30
|
2
|
|
|
|
|
|
|
|
|
|
1
|
30
|
15
|
2
|
|
|
|
|
|
|
|
|
0
|
14
|
7
|
2
|
|
|
|
|
|
|
|
|
1
|
6
|
3
|
2
|
|
|
|
|
|
|
|
|
1
|
2
|
1
|
2
|
|
|
|
|
|
|
|
|
1
|
0
|
0
|
|
|
|
|
|
|
|
|
|
1
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
|
|
|
512
|
256
|
128
|
64
|
|
16
|
8
|
4
|
|
1
|
989
|
|
|
0,375
|
*
|
2
|
|
0,750
|
|
|
0,750
|
*
|
2
|
=
|
1,500
|
|
|
0,500
|
*
|
2
|
=
|
1,000
|
|
|
|
|
|
|
|
|
989,000
|
8,000
|
|
|
|
|
984,000
|
123,000
|
8,000
|
|
|
|
5,000
|
120,000
|
15,000
|
8,000
|
|
|
3,000
|
8,000
|
1,000
|
|
|
|
7,000
|
1,000
|
|
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
|
1,000
|
7,000
|
3,000
|
5,000
|
|
3
|
|
|
|
989
|
512
|
448
|
24
|
5
|
|
0,375
|
|
0,375
|
|
|
|
|
|
989,3750
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
989,000
|
16,000
|
|
|
|
976,000
|
61,000
|
16,000
|
|
|
13,000
|
48,000
|
3,000
|
|
|
13,000
|
|
|
|
3
|
D
|
D
|
|
|
0,375
|
*
|
16
|
=
|
6,000
|
6,000
|
|
|
|
|
|
|
|
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
3
|
13
|
13
|
|
6
|
|
|
|
989
|
768
|
208
|
13
|
|
0,375
|
0
|
0,375
|
|
|
|
|
989,375
|
|
|
|
д)237,73 (10)= 11101101,10111(2)=355.5656(8)=ED.BAE(16)
|
237,0
|
2,0
|
|
|
|
|
|
|
|
|
236,0
|
118,0
|
2,0
|
|
|
|
|
|
|
|
1,0
|
118,0
|
59,0
|
2,0
|
|
|
|
|
|
|
0,0
|
58,0
|
29,0
|
2,0
|
|
|
|
|
|
|
1,0
|
28,0
|
14,0
|
2,0
|
|
|
|
|
|
|
1,0
|
14,0
|
7,0
|
2,0
|
|
|
|
|
|
|
|
0,0
|
6,0
|
3,0
|
2,0
|
|
|
|
|
|
|
1,0
|
2,0
|
1,0
|
2,0
|
|
|
|
|
|
|
1,0
|
0,0
|
0,0
|
|
|
|
|
|
|
|
1,0
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
|
|
|
|
128
|
64
|
32
|
|
8
|
4
|
|
1
|
237
|
|
|
0,730
|
*
|
2
|
|
1,460
|
|
|
0,460
|
*
|
2
|
=
|
0,920
|
|
|
0,920
|
*
|
2
|
=
|
1,840
|
|
|
0,840
|
*
|
2
|
=
|
1,680
|
|
|
0,680
|
*
|
2
|
=
|
1,360
|
|
|
237,000
|
8,000
|
|
|
|
232,000
|
29,000
|
8,000
|
|
|
5,000
|
24,000
|
3,000
|
|
|
5,000
|
3,000
|
|
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
3,1E-05
|
|
|
3,000
|
5,000
|
5,000
|
|
5
|
6
|
5
|
6
|
|
|
237
|
0
|
192
|
40
|
5
|
|
0,625
|
0,09375
|
0,00977
|
0,00146
|
0,72998
|
|
|
|
|
|
237,7300
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
237,000
|
16,000
|
|
|
224,000
|
14,000
|
|
|
13,000
|
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
|
14
|
13
|
|
11
|
10
|
14
|
|
237
|
224
|
13
|
|
0,6875
|
0,0390625
|
0,7265625
|
|
|
|
|
237,727
|
|
|
|
|
0,730
|
*
|
16
|
=
|
11,680
|
B
|
|
|
0,680
|
*
|
16
|
=
|
10,880
|
A
|
|
|
0,880
|
*
|
16
|
=
|
14,080
|
E
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
а)110001111(2)=399(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
|
|
256
|
128
|
|
|
|
8
|
4
|
2
|
1
|
399
|
б)111010001(2)=465(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
1
|
|
|
256
|
128
|
64
|
|
16
|
|
|
|
1
|
465
|
в)100110101,1001(2)=309,5625(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
1
|
|
|
256
|
|
|
32
|
16
|
|
4
|
|
1
|
309
|
|
1
|
0
|
0
|
1
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5625
|
0,5
|
0
|
0
|
0,063
|
|
|
|
|
|
|
г)1000010,01011(2)=66,34375(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
|
|
|
|
64
|
|
|
|
|
2
|
|
66
|
|
0
|
1
|
0
|
1
|
1
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
0,34375
|
0
|
0,25
|
0
|
0,063
|
0,031
|
|
|
|
|
|
д)176,5(8)=126.625(10)
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
3,1E-05
|
|
|
1,000
|
7,000
|
6,000
|
|
5
|
|
|
|
|
|
126
|
0
|
64
|
56
|
6
|
|
0,625
|
0
|
0
|
0
|
0,625
|
|
|
|
|
|
126,6250
|
|
|
|
|
|
е)3D2,04(16)=978.016(10)
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
3
|
13
|
2
|
|
0
|
4
|
|
|
978
|
768
|
208
|
2
|
|
0
|
0,015625
|
0,015625
|
|
|
|
|
978,016
|
|
|
|
|
978,000
|
16,000
|
|
|
|
976,000
|
61,000
|
16,000
|
|
|
2,000
|
48,000
|
3,000
|
|
|
13,000
|
|
|
|
0,016
|
*
|
16
|
=
|
0,256
|
0,000
|
|
|
0,256
|
*
|
16
|
=
|
4,096
|
4
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3. Сложить все числа
а)1000011101(2)+101000010(2)=541(10)+322(10)=
1101011111 (2) =863(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
|
|
512
|
0
|
0
|
0
|
0
|
16
|
8
|
4
|
0
|
1
|
541
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
|
|
0
|
256
|
0
|
64
|
0
|
0
|
0
|
0
|
2
|
0
|
322
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
863
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
+
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
|
|
|
1
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
0
|
|
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
|
|
512
|
256
|
0
|
0
|
16
|
8
|
4
|
2
|
1
|
863
|
б)100000001(2)+1000101001(2)=
257(10)+553(10)= 1100101010 (2) =810(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
|
|
0
|
256
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
257
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
|
|
512
|
0
|
0
|
0
|
32
|
0
|
8
|
0
|
0
|
1
|
553
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
810
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
+
|
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
|
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
0
|
|
|
512
|
256
|
0
|
0
|
32
|
0
|
8
|
0
|
2
|
0
|
810
|
в)101111011,01(2)+1000100,101(2)=
379,25(10)+68,625(10)= (2) =447,875(10)
|
0
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,25
|
0
|
0,25
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
|
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
|
|
|
|
|
0
|
256
|
0
|
64
|
32
|
16
|
8
|
0
|
2
|
1
|
379
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
379,25
|
|
|
|
|
|
1
|
0
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,625
|
0,5
|
0
|
0,125
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
|
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
|
|
|
|
|
0
|
0
|
0
|
64
|
0
|
0
|
0
|
4
|
0
|
0
|
68
|
|
|
|
|
68,625
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
447,875
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
+
|
|
1
|
0
|
1
|
1
|
1
|
1
|
0
|
1
|
1
|
,
|
0
|
1
|
|
|
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
,
|
1
|
0
|
1
|
|
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
,
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
|
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
|
|
|
|
|
0
|
256
|
128
|
0
|
32
|
16
|
8
|
4
|
2
|
1
|
447
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,875
|
0,5
|
0,25
|
0,125
|
|
|
|
|
|
|
|
|
|
|
|
г)1532,14(8)+730,16(8)=858.1875(10)+472.2188(10)=1330.41
(10)=2462.32172(8)
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
|
|
|
|
1,000
|
5,000
|
3,000
|
2,000
|
|
1
|
4
|
|
|
|
|
858
|
0
|
512
|
320
|
24
|
2
|
|
0,125
|
0,0625
|
0
|
|
0,1875
|
|
|
|
|
|
|
858,1875
|
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
|
|
|
|
|
7,000
|
0,000
|
|
1
|
6
|
|
|
|
|
472
|
0
|
0
|
448
|
24
|
0
|
|
0,125
|
0,09375
|
0
|
|
0,21875
|
|
|
|
|
|
|
472,2188
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
+
|
1
|
5
|
3
|
2
|
,
|
1
|
4
|
|
|
|
|
7
|
3
|
0
|
,
|
1
|
6
|
|
|
|
2
|
4
|
6
|
2
|
,
|
3
|
2
|
|
|
|
|
4+6=12
5+7=14
|
|
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
3,1E-05
|
|
|
|
2,000
|
4,000
|
6,000
|
2,000
|
|
3
|
2
|
1
|
7
|
2
|
|
1330
|
0
|
1024
|
256
|
48
|
2
|
|
0,375
|
0,03125
|
0,00195
|
0,00171
|
6,1E-05
|
|
|
|
|
|
|
|
1330,4100
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
д) BB,4(16)+2F0,6(16)= 187,25(10)+752.375(10)=939.625(10)=
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
|
11
|
11
|
|
4
|
|
|
|
187
|
0
|
176
|
11
|
|
0,25
|
0
|
0,25
|
|
|
|
|
187,250
|
|
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
2
|
15
|
0
|
|
6
|
|
|
|
752
|
512
|
240
|
0
|
|
0,375
|
0
|
0,375
|
|
|
|
|
752,375
|
|
|
|
|
+
|
2
|
F
|
0
|
,
|
6
|
|
|
|
B
|
B
|
,
|
4
|
|
|
3
|
A
|
B
|
,
|
A
|
|
|
|
10
|
11
|
|
10
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
F+B=1A
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
3
|
10
|
11
|
|
10
|
|
|
|
939
|
768
|
160
|
11
|
|
0,625
|
0
|
0,625
|
|
|
|
|
939,625
|
|
|
|
4. Выполнить вычитание
а)1000101110(2)-1111111(2)= 558(10)-127(10)= 110101111 (2) =431(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
|
|
512
|
0
|
0
|
0
|
32
|
0
|
8
|
4
|
2
|
0
|
558
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
|
0
|
0
|
0
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
127
|
|
-
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
|
|
|
|
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
|
|
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
1
|
|
|
0
|
256
|
128
|
0
|
32
|
0
|
8
|
4
|
2
|
1
|
431
|
б)1011101000(2)-1001000000(2)= 744(10)-576(10)= 10101000 (2) =168(10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
|
|
512
|
0
|
128
|
64
|
32
|
0
|
8
|
0
|
0
|
0
|
744
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
|
|
512
|
0
|
0
|
64
|
0
|
0
|
0
|
0
|
0
|
0
|
576
|
|
-
|
1
|
0
|
1
|
1
|
1
|
0
|
1
|
0
|
0
|
0
|
|
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
0
|
1
|
0
|
1
|
0
|
0
|
0
|
|
|
|
|
128
|
0
|
32
|
0
|
8
|
0
|
0
|
0
|
168
|
в)1000101001,1(2)-1111101,1(2)= 553.5(10)-125.5(10)= 110101100,0 (2) =428.0(10)
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,5
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
|
|
|
512
|
0
|
0
|
0
|
32
|
0
|
8
|
0
|
0
|
1
|
553
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
553,50
|
|
|
|
1
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,25
|
0,125
|
0,063
|
0,031
|
0,02
|
0,01
|
0,0039
|
0,002
|
0,001
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,5
|
0,5
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
|
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
|
|
|
0
|
0
|
0
|
64
|
32
|
16
|
8
|
4
|
0
|
1
|
125
|
|
|
125,500
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
428,000
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
-
|
1
|
0
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
,
|
1
|
|
|
|
|
1
|
1
|
1
|
1
|
1
|
0
|
1
|
,
|
1
|
|
|
1
|
1
|
0
|
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|
0
|
1
|
1
|
0
|
0
|
,
|
0
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
|
|
|
|
256
|
128
|
0
|
32
|
0
|
8
|
4
|
0
|
0
|
428
|
|
г)1265,2(8)-610,2(8)=693.25(10)-392.25(10)=301.00(10)=455.0(8)
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
|
|
1,000
|
2,000
|
6,000
|
5,000
|
|
2
|
|
|
|
|
693
|
0
|
512
|
128
|
48
|
5
|
|
0,25
|
0
|
0
|
0,25
|
|
|
|
|
|
|
693,2500
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
|
|
|
6,000
|
1,000
|
0,000
|
|
2
|
|
|
|
|
392
|
0
|
0
|
384
|
8
|
0
|
|
0,25
|
0
|
0
|
0,25
|
|
|
|
|
|
|
392,2500
|
|
|
|
|
|
|
|
|
|
|
|
|
|
-
|
1
|
2
|
6
|
5
|
,
|
2
|
|
|
|
6
|
1
|
0
|
,
|
2
|
|
|
|
4
|
5
|
5
|
,
|
0
|
|
|
|
8+2-6=4
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
|
|
|
|
4,000
|
5,000
|
5,000
|
|
2
|
|
|
|
|
|
301
|
0
|
0
|
256
|
40
|
5
|
|
0,25
|
0
|
0
|
0,25
|
|
|
|
|
|
|
|
301,2500
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
д) 409,D(16)-270,4(16)=1033.813(10)-624.25(10)=
409.563(10)=199.9(16)
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
4
|
0
|
9
|
|
13
|
|
|
|
1033
|
1024
|
0
|
9
|
|
0,8125
|
0
|
0,8125
|
|
|
|
|
1033,813
|
|
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,003906
|
0,000244
|
1,53E-05
|
|
2
|
7
|
0
|
|
4
|
|
|
|
|
0
|
512
|
112
|
0
|
|
0,25
|
0
|
0
|
0
|
|
624
|
|
|
|
624,2500
|
|
|
0,25
|
|
|
-
|
4
|
0
|
9
|
,
|
D
|
|
|
2
|
7
|
0
|
,
|
4
|
|
|
1
|
9
|
9
|
,
|
9
|
|
|
13-4=9
7+9=10→10-7=9
3-2=1
|
|
|
|
|
|
|
4096
|
256
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
1
|
9
|
9
|
|
9
|
|
|
|
409
|
256
|
144
|
9
|
|
0,5625
|
0
|
0,5625
|
|
|
|
|
409,563
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5. Выполнить умножение
а)111010(2)=*1100000(2)=
58(10)*96(10)= 1010111000000(2) =5568 (10)
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
|
1
|
1
|
1
|
0
|
1
|
0
|
|
|
|
|
|
32
|
16
|
8
|
0
|
2
|
0
|
58
|
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
64
|
32
|
0
|
0
|
0
|
0
|
0
|
96
|
|
|
|
|
|
*
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
|
|
1
|
1
|
1
|
0
|
1
|
0
|
|
|
|
|
|
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
0
|
0
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
|
4096
|
2048
|
1024
|
512
|
256
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
|
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
|
|
4096
|
0
|
1024
|
0
|
256
|
128
|
64
|
0
|
0
|
0
|
0
|
0
|
0
|
5568
|
б)1005.5(8)*63.3(8)= 517,6250(10)*51,3750(10)=26592.98(10)=
63740.7656(8)
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
|
|
1,000
|
0,000
|
0,000
|
5,000
|
|
5
|
|
|
|
|
517
|
0
|
512
|
0
|
0
|
5
|
|
0,625
|
0
|
0
|
0,625
|
|
|
|
|
|
|
517,6250
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,01563
|
0,00195
|
0,00024
|
|
|
|
|
6,000
|
3,000
|
|
3
|
|
|
|
|
51
|
0
|
0
|
0
|
48
|
3
|
|
0,375
|
0
|
0
|
0,375
|
|
|
|
|
|
|
51,3750
|
|
|
|
|
|
32768
|
4096
|
512
|
64
|
8
|
1
|
,
|
0,125
|
0,015625
|
0,0019531
|
0,0002441
|
|
6,000
|
3,000
|
7,000
|
4,000
|
0,000
|
|
7
|
6
|
5
|
6
|
|
26592
|
24576
|
1536
|
448
|
32
|
0
|
|
0,875
|
0,09375
|
0,0097656
|
0,9785156
|
|
|
|
|
|
|
26592,9785
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*
|
1
|
0
|
0,
|
5
|
5
|
|
|
|
|
|
|
6,
|
3
|
3
|
|
|
|
|
3
|
0
|
2
|
0
|
7
|
|
|
|
3
|
0
|
2
|
0
|
7
|
|
|
|
6
|
0
|
4
|
2
|
6
|
|
|
|
|
6
|
3
|
7
|
4
|
0,
|
7
|
7
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3*5=17
3*5+1=17+1=18→(2)0
3*0+2=2
3*0=0
3*1=3
2+6=0
6*5=36
6*5+6=(4)2
6*0+4=4
6*0=0
6*1=6
в)4A,3(16)*F,6(16)= 74.188(10)*15.375(10)=1140.64(10)=474.A2(16)
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
|
4
|
10
|
|
3
|
|
|
|
74
|
0
|
64
|
10
|
|
0,1875
|
0
|
0,1875
|
|
|
|
|
74,188
|
|
|
|
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
|
|
15
|
|
6
|
|
|
|
15
|
0
|
0
|
15
|
|
0,375
|
0
|
0,375
|
|
|
|
|
15,375
|
|
|
|
|
*
|
4
|
A,
|
3
|
|
|
|
|
F,
|
6
|
|
|
1
|
B
|
D
|
2
|
|
|
4
|
8
|
D
|
|
|
|
4
|
7
|
4,
|
A
|
2
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6*3=18=1*16+2
6*A=60+1=61=3*16+13→D
6*4=24+3=27=1*16+11→B
F*3=15*3=45=2*16+13→D
F*A=15*10=150+2=9*16+8
F*4=15*4=60+9=69=4*16+5
2+0=2
13+13=26=1*16+10→A
11+8=19+1=20=1*16+4
1+5+1=7
4
|
4096
|
256
|
16
|
1
|
,
|
0,0625
|
0,0039063
|
0,0002441
|
|
4
|
7
|
4
|
|
10
|
2
|
|
|
1140
|
1024
|
112
|
4
|
|
0,625
|
0,0078125
|
0,6328125
|
|
|
|
|
1140,633
|
|
|
|
1)
Пономарёв В.С.,
Красников В.В. Методические указания по теме: "Арифметические основы
ЭВМ":http://www.rus-edu.bg/edu/online/inf/bookinf/theory/chapter4/1_4_10.html
4)
Системы
счисления Анжелиной Латышевой : http://logika.weebly.com/10571083108610781077108510801077-1074-107410861089110010841077108810801095108510861081-1089108010891090107710841077.html