Question

Выполните сложение в двоичной системе счисления 1111+1  выполните умножение в двоичной системе счисления 1110*101

Answer 1

Сложение:
1111 + 1 = 10000

Умножение:
1110*101 = 1000110

Answer 2

Addition in Binary System

To perform addition in the binary system, we add the binary digits from right to left, just like in decimal addition. If the sum of two digits is 0 or 1, we write that digit as the result. If the sum is 2, we write 0 and carry over 1 to the next column. Here's how we can add the binary numbers 1111 and 1:

  1111
+    1
------

Starting from the rightmost column, we add the digits:

  1111
+    1
------
 10000

The result of adding 1111 and 1 in the binary system is 10000.

Multiplication in Binary System

To perform multiplication in the binary system, we use a method similar to long multiplication in decimal. We multiply each digit of the second number by each digit of the first number, and then add the partial products. Let's multiply 1110 and 101:

    1110
  x  101
-------

We start by multiplying the rightmost digit of the second number (1) by each digit of the first number:

    1110
  x  101
-------
    1110   (partial product)

Next, we multiply the second digit of the second number (0) by each digit of the first number, shifting one place to the left:

    1110
  x  101
-------
    1110   (partial product)
   0000    (partial product, shifted one place to the left)

Finally, we multiply the third digit of the second number (1) by each digit of the first number, shifting two places to the left:

``` 111