How is a decimal number converted to its binary equivalent?

How is a decimal number converted to its binary equivalent?

• A. By sequentially dividing the number by 2 and recording each remainder
• B. By multiplying the number by 2 and recording remainders
• C. By subtracting powers of two from the number
• D. By converting to hexadecimal first and then to binary

Answer: (A)

Converting a decimal number to binary is done by repeatedly dividing the number by 2 and recording the remainders. Each division reveals the next binary digit, starting with the least significant bit. When the quotient eventually becomes zero, you read the recorded remainders in reverse order to get the binary representation. For example, take 13. 13 ÷ 2 gives quotient 6 and remainder 1; 6 ÷ 2 gives quotient 3 and remainder 0; 3 ÷ 2 gives quotient 1 and remainder 1; 1 ÷ 2 gives quotient 0 and remainder 1. Reading the remainders from last to first yields 1101, so 13 in binary is 1101. Multiplying by 2 and recording remainders isn’t the correct method for constructing binary digits. Subtracting powers of two from the number can help identify which bits are set, but it doesn’t provide the full step-by-step conversion. Converting to hexadecimal first and then to binary can work as a shortcut (each hex digit maps to four binary digits), but it adds an extra step and isn’t the direct method.

Converting a decimal number to binary is done by repeatedly dividing the number by 2 and recording the remainders. Each division reveals the next binary digit, starting with the least significant bit. When the quotient eventually becomes zero, you read the recorded remainders in reverse order to get the binary representation.

For example, take 13. 13 ÷ 2 gives quotient 6 and remainder 1; 6 ÷ 2 gives quotient 3 and remainder 0; 3 ÷ 2 gives quotient 1 and remainder 1; 1 ÷ 2 gives quotient 0 and remainder 1. Reading the remainders from last to first yields 1101, so 13 in binary is 1101.

Multiplying by 2 and recording remainders isn’t the correct method for constructing binary digits. Subtracting powers of two from the number can help identify which bits are set, but it doesn’t provide the full step-by-step conversion. Converting to hexadecimal first and then to binary can work as a shortcut (each hex digit maps to four binary digits), but it adds an extra step and isn’t the direct method.