subtract in the indicated base.

\
\begin{array}{r}
1101_{2} \\
-\quad 111_{2} \\
\hline
\end{array}
\

Question

subtract in the indicated base.

\
\begin{array}{r}
1101_{2} \\
-\quad 111_{2} \\
\hline
\end{array}
\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Binary Numbers" ], "new_concepts": [], "current_concepts": [ "Binary Numbers", "Base Conversion" ] } ## Align the numbers vertically Using the *Binary Numbers* knowledge point $$ \begin{array}{r@{\quad}l} 1101_2 \ - \phantom{0}111_2 \ \hline \end{array} $$ ## Subtract the ones column Using the *Binary Numbers* knowledge point $$ 1_2 - 1_2 = 0_2 $$ ## Subtract the twos column with borrowing Using the *Binary Numbers* knowledge point $$ \begin{aligned} &\text{Borrow from the fours column (reducing } 1 \text{ to } 0\text{):}\ &(0_2 + 10_2) - 1_2 = 2_{10} - 1_{10} = 1_2 \end{aligned} $$ ## Subtract the fours column with borrowing Using the *Binary Numbers* knowledge point $$ \begin{aligned} &\text{Borrow from the eights column (reducing } 1 \text{ to } 0\text{):}\ &(0_2 + 10_2) - 1_2 = 2_{10} - 1_{10} = 1_2 \end{aligned} $$ ## Combine the column results Using the *Binary Numbers* knowledge point $$ 1101_2 - 111_2 = 110_2 $$ Subtract in the indicated base. $$ \begin{array}{r@{\quad}l} 1101_2 \ - \phantom{0}111_2 \ \hline \end{array} $$ $110_2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Binary Numbers" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Align the numbers vertically

Subtract the ones column

Subtract the twos column with borrowing

Subtract the fours column with borrowing

Combine the column results

Answer: