Question

Помогите пожалуйста! Вообще никак не понимаю(1) Переведите 10977 из десятичной в четверичную систему счисления.2) Сравните числа III и 111, записанные в римской и двоичной системах счисления.

Answer 1

1)2223201
2) 111 в 2-ой = 7 в 10-ой
  III - 3 в десятичной ⇒
111 больше  III

Answer 2

Converting 10977 from decimal to quaternary (base-4) system:

To convert a decimal number to the quaternary system, we need to divide the decimal number by 4 repeatedly and record the remainders. The remainders will be the digits of the quaternary representation, read from bottom to top.

Let's convert 10977 to the quaternary system:

1. Divide 10977 by 4: 10977 ÷ 4 = 2744 remainder 1. Record the remainder 1. 2. Divide 2744 by 4: 2744 ÷ 4 = 686 remainder 0. Record the remainder 0. 3. Divide 686 by 4: 686 ÷ 4 = 171 remainder 2. Record the remainder 2. 4. Divide 171 by 4: 171 ÷ 4 = 42 remainder 3. Record the remainder 3. 5. Divide 42 by 4: 42 ÷ 4 = 10 remainder 2. Record the remainder 2. 6. Divide 10 by 4: 10 ÷ 4 = 2 remainder 2. Record the remainder 2. 7. Divide 2 by 4: 2 ÷ 4 = 0 remainder 2. Record the remainder 2.

Reading the remainders from bottom to top, the quaternary representation of 10977 is 2223221.

Therefore, 10977 in decimal is equal to 2223221 in the quaternary system.

Comparing the numbers III and 111 in Roman and binary numeral systems:

To compare the numbers III and 111 in the Roman and binary numeral systems, we need to understand the values represented by each numeral.

In the Roman numeral system: - III represents the number 3. Each "I" represents 1, and when they are combined, they add up to 3.

In the binary numeral system: - 111 represents the number 7. Each digit in binary represents a power of 2, starting from the rightmost digit. In this case, the rightmost digit is 1, which represents 2^0 (1). The next digit is 1, which represents 2^1 (2). The leftmost digit is also 1, which represents 2^2 (4). Adding these values together gives us 7.

Therefore, in the Roman numeral system, III is equal to 3, and in the binary numeral system, 111 is equal to 7.

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