Solution - Base conversion

1, 440

1,440

Step-by-step explanation

${(5 A 0)}_{16} = b a s e 10$

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

${(5 A 0)}_{16} = 5 \cdot 16^{2} + 10 \cdot 16^{1} + 0 \cdot 16^{0}$

$5 \cdot 16^{2} + 10 \cdot 16^{1} + 0 \cdot 16^{0} = 1440$

Expand each digit by place value: $5 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $0 \cdot 16^{0}$ . This gives $1, 440$ in base 10.

$\frac{1440}{10} = 144 r e m a \in d e r 0$

$\frac{144}{10} = 14 r e m a \in d e r 4$

$\frac{14}{10} = 1 r e m a \in d e r 4$

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

$0 \to 4 \to 4 \to 1 = 1440$

$1440 (b a s e 10) = {(1440)}_{10}$

Repeatedly divide $1, 440$ by $10$ , collect remainders, and read them in reverse to get $1, 440$ .

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