To convert a decimal number to binary, which procedure is standard?

To convert a decimal number to binary, which procedure is standard?

• A. Use Positional Notation
• B. Divide by 2, Use Remainders
• C. Group Binary Number into 3s, Use Table
• D. Group Binary Number into 4s, Use Table

Answer: (B)

Dividing by 2 and recording the remainders is the standard way to convert a decimal number to binary. Each division reveals the next least-significant bit, and when you read the remainders from bottom to top you get the binary representation. For example, converting 13: 13 ÷ 2 = 6 with remainder 1, 6 ÷ 2 = 3 with remainder 0, 3 ÷ 2 = 1 with remainder 1, 1 ÷ 2 = 0 with remainder 1. Reading the remainders upward gives 1101₂. Grouping binary digits into fours or threes with a table is a shortcut used when converting between binary and other bases like hexadecimal (four bits per hex digit) or octal (three bits per octal digit), not the standard decimal-to-binary process. Using the idea of positional notation is the underlying principle of all number systems, but the concrete method for decimal to binary is the repeated division by 2 with remainders.

Dividing by 2 and recording the remainders is the standard way to convert a decimal number to binary. Each division reveals the next least-significant bit, and when you read the remainders from bottom to top you get the binary representation. For example, converting 13: 13 ÷ 2 = 6 with remainder 1, 6 ÷ 2 = 3 with remainder 0, 3 ÷ 2 = 1 with remainder 1, 1 ÷ 2 = 0 with remainder 1. Reading the remainders upward gives 1101₂.

Grouping binary digits into fours or threes with a table is a shortcut used when converting between binary and other bases like hexadecimal (four bits per hex digit) or octal (three bits per octal digit), not the standard decimal-to-binary process. Using the idea of positional notation is the underlying principle of all number systems, but the concrete method for decimal to binary is the repeated division by 2 with remainders.