Question

Закодировать десятичные числа нулями и единицами (перевести десятичное число в двоичное): А) 53 Б) 64 2) Раскодировать двоичный код в десятичное число (перевести двоичное число в десятичное): А) 〖1000 0001〗_2 Б) 〖0010 0011〗_2

Answer 1

Ответ:

a)53= 110101_2

б)1000000_2

a)129_2

Б)17_2

Answer 2

Закодировать десятичные числа нулями и единицами (перевести десятичное число в двоичное):

А) 53

To convert the decimal number 53 into binary, we can use the following steps:

1. Divide the decimal number by 2 and note down the remainder. 2. Divide the quotient obtained in step 1 by 2 and note down the remainder. 3. Repeat step 2 until the quotient becomes 0. 4. The binary representation of the decimal number is obtained by arranging the remainders obtained in reverse order.

Let's apply these steps to convert 53 into binary:

- Step 1: 53 divided by 2 equals 26 with a remainder of 1. - Step 2: 26 divided by 2 equals 13 with a remainder of 0. - Step 3: 13 divided by 2 equals 6 with a remainder of 1. - Step 4: 6 divided by 2 equals 3 with a remainder of 0. - Step 5: 3 divided by 2 equals 1 with a remainder of 1. - Step 6: 1 divided by 2 equals 0 with a remainder of 1.

The remainders in reverse order are 110101. Therefore, the binary representation of the decimal number 53 is 110101. Б) 64

To convert the decimal number 64 into binary, we can follow the same steps as above:

- Step 1: 64 divided by 2 equals 32 with a remainder of 0. - Step 2: 32 divided by 2 equals 16 with a remainder of 0. - Step 3: 16 divided by 2 equals 8 with a remainder of 0. - Step 4: 8 divided by 2 equals 4 with a remainder of 0. - Step 5: 4 divided by 2 equals 2 with a remainder of 0. - Step 6: 2 divided by 2 equals 1 with a remainder of 0. - Step 7: 1 divided by 2 equals 0 with a remainder of 1.

The remainders in reverse order are 1000000. Therefore, the binary representation of the decimal number 64 is 1000000.

Раскодировать двоичный код в десятичное число (перевести двоичное число в десятичное):

А) 〖1000 0001〗_2

To convert the binary number 10000001 into decimal, we can use the following steps:

1. Start from the rightmost digit and assign a value of 1 to it. 2. Multiply this value by 2 raised to the power of the position of the digit (starting from 0 for the rightmost digit). 3. Repeat steps 1 and 2 for each digit, adding the results together.

Let's apply these steps to convert 10000001 into decimal:

- The rightmost digit is 1, so we assign a value of 1 to it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The leftmost digit is 1, so we assign a value of 1 to it.

Now, let's calculate the decimal value:

1 * 2^7 + 1 * 2^0 = 128 + 1 = 129

Therefore, the decimal representation of the binary number 10000001 is 129. Б) 〖0010 0011〗_2

To convert the binary number 00100011 into decimal, we can follow the same steps as above:

- The rightmost digit is 1, so we assign a value of 1 to it. - The next digit to the left is 1, so we assign a value of 2 to it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 0, so we skip it. - The next digit to the left is 1, so we assign a value of 16 to it. - The next digit to the left is 0, so we skip it. - The leftmost digit is 0, so we skip it.

Now, let's calculate the decimal value:

1 * 2^5 + 1 * 2^4 + 1 * 2^1 + 1 * 2^0 = 32 + 16 + 2 + 1 = 51

Therefore, the decimal representation of the binary number 00100011 is 51.