Solution - Base conversion

1, 185

1,185

Step-by-step explanation

${(4 A 1)}_{16} = b a s e 10$

Identify the source number, source base, and target base before converting through base 10.

${(4 A 1)}_{16} = 4 \cdot 16^{2} + 10 \cdot 16^{1} + 1 \cdot 16^{0}$

$4 \cdot 16^{2} + 10 \cdot 16^{1} + 1 \cdot 16^{0} = 1185$

Expand each digit by place value: $4 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $1 \cdot 16^{0}$ . This gives $1, 185$ in base 10.

$\frac{1185}{10} = 118 r e m a \in d e r 5$

$\frac{118}{10} = 11 r e m a \in d e r 8$

$\frac{11}{10} = 1 r e m a \in d e r 1$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$5 \to 8 \to 1 \to 1 = 1185$

$1185 (b a s e 10) = {(1185)}_{10}$

Repeatedly divide $1, 185$ by $10$ , collect remainders, and read them in reverse to get $1, 185$ .

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Base conversion is foundational for computer science, digital systems, and number theory.