Question

Помогите! Двоичная и десятичная система счисления321

Answer 1

321 в десятичной = 101000001 в двоичной

Answer 2

Binary and Decimal Number Systems

The binary and decimal number systems are two commonly used systems for representing numbers.

Decimal System: The decimal system, also known as the base-10 system, is the number system most familiar to us. It uses ten digits (0-9) to represent numbers. Each digit's position in a decimal number represents a power of 10. For example, in the number 321, the digit 3 represents 3 hundreds (10^2), the digit 2 represents 2 tens (10^1), and the digit 1 represents 1 unit (10^0).

Binary System: The binary system, also known as the base-2 system, is used in computer systems and digital electronics. It uses only two digits (0 and 1) to represent numbers. Each digit's position in a binary number represents a power of 2. For example, in the binary number 1010, the leftmost digit represents 1 eight (2^3), the second digit represents 0 fours (2^2), the third digit represents 1 two (2^1), and the rightmost digit represents 0 ones (2^0).

To convert a decimal number to binary, you can use the process of repeated division by 2. Here's an example:

1. Start with the decimal number 321. 2. Divide 321 by 2, resulting in a quotient of 160 and a remainder of 1. 3. Divide 160 by 2, resulting in a quotient of 80 and a remainder of 0. 4. Divide 80 by 2, resulting in a quotient of 40 and a remainder of 0. 5. Divide 40 by 2, resulting in a quotient of 20 and a remainder of 0. 6. Divide 20 by 2, resulting in a quotient of 10 and a remainder of 0. 7. Divide 10 by 2, resulting in a quotient of 5 and a remainder of 0. 8. Divide 5 by 2, resulting in a quotient of 2 and a remainder of 1. 9. Divide 2 by 2, resulting in a quotient of 1 and a remainder of 0. 10. Divide 1 by 2, resulting in a quotient of 0 and a remainder of 1.

Reading the remainders from bottom to top gives us the binary representation of 321, which is 101000001.

To convert a binary number to decimal, you can use the process of multiplying each digit by the corresponding power of 2 and summing the results. Here's an example:

1. Start with the binary number 101000001. 2. Multiply the leftmost digit (1) by 2^8, resulting in 256. 3. Multiply the second digit (0) by 2^7, resulting in 0. 4. Multiply the third digit (1) by 2^6, resulting in 64. 5. Multiply the fourth digit (0) by 2^5, resulting in 0. 6. Multiply the fifth digit (0) by 2^4, resulting in 0. 7. Multiply the sixth digit (0) by 2^3, resulting in 0. 8. Multiply the seventh digit (0) by 2^2, resulting in 0. 9. Multiply the eighth digit (0) by 2^1, resulting in 0. 10. Multiply the rightmost digit (1) by 2^0, resulting in 1.

Summing the results gives us the decimal representation of 101000001, which is 321.

I hope this explanation helps! Let me know if you have any further questions.