Системы счисления. Перевод двоичной и десятичной.

Maya пытается преобразовать число 101 из двоичной в десятичную систему. Каков результат?

• 3

• 7

• 5

• 9

Answer explanation

Число 101 в двоичной системе счисления эквивалентно 5 в десятичной. Чтобы преобразовать, вы умножаете каждую цифру справа налево на 2, возведенные в степень ее положения, а затем суммируете результаты: (1*2^2) + (0*2^1) + (1*2^0) = 5.

Переведите число 13 в двоичную систему счисления

• 1110

• 1001

• 1011

• 1101

Answer explanation

The correct binary equivalent of 13 in decimal is 1101. Each digit in binary represents a power of 2, starting from the right with 2^0. Therefore, 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 13.

What is the decimal equivalent of the binary number 1101?

• 13

• 14

• 16

• 15

Answer explanation

The number 1101 in binary is equivalent to 13 in decimal. To convert from binary to decimal, you multiply each digit by 2 raised to the power of its position from right to left, then sum the results.

Convert the binary number 1111 to decimal.

• 13

• 17

• 19

• 15

Answer explanation

To convert 1111 from binary to decimal, we use the formula: (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 4 + 2 + 1 = 15. Therefore, the correct answer is 15.

What is the binary equivalent of the decimal number 25?

• 11100

• 10101

• 11001

• 10011

Answer explanation

The correct binary equivalent of 25 in decimal is 11001, which matches the option '11001'.

What is the value of the number 10001 in the decimal number system?

• 11

• 15

• 17

• 23

Answer explanation

The number 10001 in decimal system equals 17. This is the correct choice among the options provided.

Convert the number 0101 from binary to decimal.

• 11

• 5

• 100

• 10

Answer explanation

To convert 0101 from binary to decimal, we use the formula: (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 10

What is the binary equivalent of the number 42 in decimal system?

• 110101

• 111000

• 101010

• 100100

Answer explanation

The correct binary equivalent of 42 in decimal is 101010, which matches the given choice.

What is the decimal equivalent of the binary number 10101?

• 22

• 23

• 20

• 21

Answer explanation

The number 10101 in binary is equivalent to 21 in decimal. To convert, multiply each digit by 2 raised to the power of its position from right to left: 1*2^0 + 0*2^1 + 1*2^2 + 0*2^3 + 1*2^4 = 21.

Convert the binary number 1100 to decimal.

• 12

• 16

• 10

• 14

Answer explanation

To convert 1100 from binary to decimal, we use the formula: (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 8 + 4 = 12. Therefore, the correct answer is 12.