Answer:
The total number of cups of coffee sold are 51 which can be expressed in base [tex]2[/tex] as [tex]110011[/tex].
Step-by-step explanation:
Considering the following information
- [tex]1[/tex] cup = [tex]1[/tex] cup
- [tex]7[/tex] pints = [tex]14[/tex] cups ∵ [tex]1[/tex] pint = [tex]2[/tex] cups
- [tex]9[/tex] quarts = [tex]36[/tex] cups ∵ [tex]1[/tex] quart = [tex]4[/tex] cups
So, total number of cups will be = [tex]51[/tex] cups
Converting [tex]51[/tex] to the base [tex]2[/tex]
Divide [tex]51[/tex] by [tex]2[/tex] by repeatedly and observe remainder
[tex]\frac{51}{2}=25\quad \mathrm{Remainder}\quad \:1[/tex]
[tex]\frac{25}{2}=12\quad \mathrm{Remainder}\quad \:1[/tex]
[tex]\frac{12}{2}=6\quad \mathrm{Remainder}\quad \:0[/tex]
[tex]\frac{6}{2}=3\quad \mathrm{Remainder}\quad \:0[/tex]
[tex]\frac{3}{2}=1\quad \mathrm{Remainder}\quad \:1[/tex]
[tex]\frac{1}{2}=0\quad \mathrm{Remainder}\quad \:1[/tex]
Read and observe the remainder from top to bottom would yield [tex]110011[/tex].
Therefore, the total number of cups of coffee sold are 51 which can be expressed in base [tex]2[/tex] as [tex]110011[/tex].
Keywords: base 2, number
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