Question

Дано: а = 5D16, b = 1378. Какое из чисел х, записанных в двоичной системе, отвечает уравнению a < x < b? 1) 10111102 2) 10011012 3) 10011112 4) 10111002 Ответ: Переведем числа в двоичную систему счисления и затем сравним их: 5D16 = 10111012 1378 = 10111112 Вопрос: при переводе числа 137^8 в двоичную систему счисления, получается число 111111. Это 6 цифр, а 5D = 7 и в ответе 7. Как при переводе получилось 7 цифр ? Откуда там 0?

Answer 1

137 (8сс)=1 011 111 (2сс)                (  3  (8cc) =011 (2cc)  !!!  по триадам!!! )
                  1  3    7

5D (16сс) = 101 1101 (2сс)
                     5      D

  101 1101 <  101 1111
5D (16cc)   <   137 (8cc)

Answer 2

There seems to be a misunderstanding in your calculation. Let's clarify the process of converting the number 1378 to binary.

To convert the decimal number 1378 to binary, we use the process of successive division by 2 and noting the remainders:

1. Divide 137 by 2: Quotient = 68, Remainder = 1
2. Divide 68 by 2: Quotient = 34, Remainder = 0
3. Divide 34 by 2: Quotient = 17, Remainder = 0
4. Divide 17 by 2: Quotient = 8, Remainder = 1
5. Divide 8 by 2: Quotient = 4, Remainder = 0
6. Divide 4 by 2: Quotient = 2, Remainder = 0
7. Divide 2 by 2: Quotient = 1, Remainder = 0
8. Divide 1 by 2: Quotient = 0, Remainder = 1

Now, read the remainders from bottom to top: 100010012

So, the binary representation of 1378 is 100010012.

Now, we need to find a binary number x that satisfies the inequality 5D16 (which is equivalent to 5D16) < x < 1378.

5D16 = 10111012 1378 = 100010012

The options given are:

1. 10111102
2. 10011012
3. 10011112
4. 10111002

Now, let's convert each option to decimal:

1. 10111102 = 95 (in decimal)
2. 10011012 = 77 (in decimal)
3. 10011112 = 79 (in decimal)
4. 10111002 = 122 (in decimal)

Now, we need to find a number that satisfies the inequality 95 < x < 1378. The only option that fulfills this condition is 10011112, which is equal to 79 in decimal.

So, the correct answer is: 3) 10011112