Question

30 баллов! Надо перевести из "10" системы счисления (с.c) в "2" с.с. 5 чисел: 20 68 400 257 2010

Answer 1

Ответ:

1) 20₁₀ = 10100₂

2) 68₁₀ = 1000100₂

3) 400₁₀ = 110010000₂

4) 257₁₀ = 100000001₂

5) 2010₁₀ = 11111011010₂

Объяснение:

1) 20₁₀ = n₂

20 mod 2 = 0

10 mod 2 = 0

5 mod 2 = 1

2 mod 2 = 0

1 mod 2 = 1

Остаток от деления записываем в обратном порядке и получаем число: 10100₂

2) 68₁₀ = n₂

68 mod 2 = 0

34 mod 2 = 0

17 mod 2 = 1

8 mod 2 = 0

4 mod 2 = 0

2 mod 2 = 0

1 mod 2 = 1

Остаток от деления записываем в обратном порядке и получаем число: 1000100₂

3) 400₁₀ = n₂

400 mod 2 = 0

200 mod 2 = 0

100 mod 2 = 0

50 mod 2 = 0

25 mod 2 = 1

12 mod 2 = 0

6 mod 2 = 0

3 mod 2 = 1

1 mod 2 = 1

Остаток от деления записываем в обратном порядке и получаем число: 110010000₂

4) 257₁₀ = n₂

257 mod 2 = 1

128 mod 2 = 0

64 mod 2 = 0

32 mod 2 = 0

16 mod 2 = 0

8 mpod 2 = 0

4 mod 2 = 0

2 mod 2 = 0

1 mod 2 = 1

Остаток от деления записываем в обратном порядке и получаем число: 100000001₂

5) 2010₁₀ = n₂

2010 mod 2 = 0

1005 mod 2 = 1

502 mod 2 = 0

251 mod 2 = 1

125 mod 2 = 1

62 mod 2 = 0

31 mod 2 = 1

15 mod 2 = 1

7 mod 2 = 1

3 mod 2 = 1

1 mod 2 = 1

Остаток от деления записываем в обратном порядке и получаем число: 11111011010₂

Answer 2

Converting from Base-10 to Base-2

To convert numbers from base-10 to base-2 (binary), we can use the following steps:

1. Divide the decimal number by 2. 2. Write down the remainder (0 or 1). 3. Divide the quotient obtained in step 1 by 2 again. 4. Repeat steps 2 and 3 until the quotient becomes 0. 5. The binary representation of the number is obtained by writing down the remainders in reverse order.

Let's apply these steps to convert the given numbers from base-10 to base-2:

1. Number: 20 - Divide 20 by 2: 20 ÷ 2 = 10, remainder 0. - Divide 10 by 2: 10 ÷ 2 = 5, remainder 0. - Divide 5 by 2: 5 ÷ 2 = 2, remainder 1. - Divide 2 by 2: 2 ÷ 2 = 1, remainder 0. - Divide 1 by 2: 1 ÷ 2 = 0, remainder 1. - The binary representation of 20 is 10100.

2. Number: 68 - Divide 68 by 2: 68 ÷ 2 = 34, remainder 0. - Divide 34 by 2: 34 ÷ 2 = 17, remainder 0. - Divide 17 by 2: 17 ÷ 2 = 8, remainder 1. - Divide 8 by 2: 8 ÷ 2 = 4, remainder 0. - Divide 4 by 2: 4 ÷ 2 = 2, remainder 0. - Divide 2 by 2: 2 ÷ 2 = 1, remainder 0. - Divide 1 by 2: 1 ÷ 2 = 0, remainder 1. - The binary representation of 68 is 1000100.

3. Number: 400 - Divide 400 by 2: 400 ÷ 2 = 200, remainder 0. - Divide 200 by 2: 200 ÷ 2 = 100, remainder 0. - Divide 100 by 2: 100 ÷ 2 = 50, remainder 0. - Divide 50 by 2: 50 ÷ 2 = 25, remainder 0. - Divide 25 by 2: 25 ÷ 2 = 12, remainder 1. - Divide 12 by 2: 12 ÷ 2 = 6, remainder 0. - Divide 6 by 2: 6 ÷ 2 = 3, remainder 0. - Divide 3 by 2: 3 ÷ 2 = 1, remainder 1. - Divide 1 by 2: 1 ÷ 2 = 0, remainder 1. - The binary representation of 400 is 110010000.

4. Number: 257 - Divide 257 by 2: 257 ÷ 2 = 128, remainder 1. - Divide 128 by 2: 128 ÷ 2 = 64, remainder 0. - Divide 64 by 2: 64 ÷ 2 = 32, remainder 0. - Divide 32 by 2: 32 ÷ 2 = 16, remainder 0. - Divide 16 by 2: 16 ÷ 2 = 8, remainder 0. - Divide 8 by 2: 8 ÷ 2 = 4, remainder 0. - Divide 4 by 2: 4 ÷ 2 = 2, remainder 0. - Divide 2 by 2: 2 ÷ 2 = 1, remainder 0. - Divide 1 by 2: 1 ÷ 2 = 0, remainder 1. - The binary representation of 257 is 100000001.

5. Number: 2010 - Divide 2010 by 2: 2010 ÷ 2 = 1005, remainder 0. - Divide 1005 by 2: 1005 ÷ 2 = 502, remainder 1. - Divide 502 by 2: 502 ÷ 2 = 251, remainder 0. - Divide 251 by 2: 251 ÷ 2 = 125, remainder 1. - Divide 125 by 2: 125 ÷ 2 = 62, remainder 1. - Divide 62 by 2: 62 ÷ 2 = 31, remainder 0. - Divide 31 by 2: 31 ÷ 2 = 15, remainder 1. - Divide 15 by 2: 15 ÷ 2 = 7, remainder 1. - Divide 7 by 2: 7 ÷ 2 = 3, remainder 1. - Divide 3 by 2: 3 ÷ 2 = 1, remainder 1. - Divide 1 by 2: 1 ÷ 2 = 0, remainder 1. - The binary representation of 2010 is 11111011010.

I hope this helps! Let me know if you have any further questions.