Question

Перевести число 173 из десятичной системы счисления в двоичную. Перевести число 110111011из двоичной системы счисления в десятичную. Записать представление числа -115 в однобайтовой ячейке. Выполнить сложение в двоичной системе счисления: 110101+10101, 11010+11001 Выполнить умножение в двоичной системе счисления: 110101+10101, 11010+11001

Answer 1

173---> 10101101
110111011---> 443
про -115 не знаю
110101+10101--->1101010
11010+11001--->110011
110101*10101--->10001011001
11010*11001--->1010001010

Answer 2

Converting Decimal to Binary

To convert a decimal number to binary, you can use the following steps: 1. Divide the decimal number by 2. 2. Write down the remainder (0 or 1). 3. Repeat steps 1 and 2 with the quotient until the quotient becomes 0. 4. The binary representation is the sequence of remainders in reverse order.

Let's apply these steps to convert the decimal number 173 to binary: 1. 173 divided by 2 is 86 with a remainder of 1. 2. 86 divided by 2 is 43 with a remainder of 0. 3. 43 divided by 2 is 21 with a remainder of 1. 4. 21 divided by 2 is 10 with a remainder of 1. 5. 10 divided by 2 is 5 with a remainder of 0. 6. 5 divided by 2 is 2 with a remainder of 1. 7. 2 divided by 2 is 1 with a remainder of 0. 8. 1 divided by 2 is 0 with a remainder of 1.

Therefore, the binary representation of 173 is 10101101.

Converting Binary to Decimal

To convert a binary number to decimal, you can use the following steps: 1. Start from the rightmost digit of the binary number. 2. Multiply each digit by 2 raised to the power of its position (starting from 0 for the rightmost digit). 3. Sum up the results of each multiplication.

Let's apply these steps to convert the binary number 110111011 to decimal: 1. Starting from the rightmost digit, the first digit is 1. Multiply it by 2^0, which is 1. 2. The second digit is 1. Multiply it by 2^1, which is 2. 3. The third digit is 0. Multiply it by 2^2, which is 4. 4. Continue this process for each digit, multiplying by increasing powers of 2. 5. Sum up the results: 1 + 2 + 0 + 8 + 16 + 32 + 64 + 128 = 251.

Therefore, the decimal representation of 110111011 is 251.

Representing -115 in a One-Byte Cell

In a one-byte cell, the range of representable values depends on the number of bits used. A one-byte cell typically consists of 8 bits, allowing for the representation of values from -128 to 127.

To represent -115 in a one-byte cell, we can use the two's complement representation. In this representation, the leftmost bit (the most significant bit) is used as the sign bit, with 0 representing a positive number and 1 representing a negative number.

To find the two's complement representation of -115 in a one-byte cell: 1. Convert the absolute value of the number (115) to binary: 01110011. 2. Invert all the bits: 10001100. 3. Add 1 to the inverted value: 10001101.

Therefore, the two's complement representation of -115 in a one-byte cell is 10001101.

Binary Addition: 110101 + 10101

To perform binary addition, you can use the following steps: 1. Start from the rightmost digits of the two binary numbers. 2. Add the corresponding digits, along with any carry from the previous addition. 3. Write down the sum digit and determine the carry for the next addition. 4. Repeat steps 2 and 3 for each pair of digits, moving from right to left. 5. If there is a carry after the leftmost addition, include it in the result.

Let's perform the binary addition of 110101 and 10101: ``` 110101 + 10101 --------- 1001000 ```

Therefore, the sum of 110101 and 10101 in binary is 1001000.

Binary Multiplication: 110101 * 10101

To perform binary multiplication, you can use the following steps: 1. Start from the rightmost digit of the second binary number. 2. Multiply the first binary number by the current digit of the second binary number, shifting the result to the left according to the position of the digit. 3. Sum up the results of each multiplication.

Let's perform the binary multiplication of 110101 and 10101: ``` 110101 * 10101 ----------- 110101 (Partial product: 110101 * 1) + 1101010 (Partial product: 110101 * 0, shifted 1 position to the left) [phone] (Partial product: 110101 * 1, shifted