convert 23 to a numeral in base 2.

$23 = \square_{2}$

Question

convert 23 to a numeral in base 2.

$23 = \square_{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Base Conversion", "Binary Numbers" ], "current_concepts": [ "Base Conversion", "Binary Numbers" ] } ## Identify the conversion method We need to convert the decimal number $23$ into base 2 (binary). We will use successive division by 2. ## Perform successive division We divide the number by 2 repeatedly and record the remainders. $$ \begin{aligned} 23 \div 2 &= 11 \quad \text{remainder } 1 \ 11 \div 2 &= 5 \quad \text{remainder } 1 \ 5 \div 2 &= 2 \quad \text{remainder } 1 \ 2 \div 2 &= 1 \quad \text{remainder } 0 \ 1 \div 2 &= 0 \quad \text{remainder } 1 \end{aligned} $$ ## Construct the binary number We read the remainders from the bottom to the top to get the binary representation. $$ 23_{10} = 10111_2 $$ Convert 23 to a numeral in base 2. $23 =$ 10111$_2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Number Theory", "Base Conversion" ] }

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Question

Explanation:

Identify the conversion method

Perform successive division

Construct the binary number

Answer: