Solution - Base conversion

1, 763

1,763

Step-by-step explanation

${(6 E 3)}_{16} = b a s e 10$

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

${(6 E 3)}_{16} = 6 \cdot 16^{2} + 14 \cdot 16^{1} + 3 \cdot 16^{0}$

$6 \cdot 16^{2} + 14 \cdot 16^{1} + 3 \cdot 16^{0} = 1763$

Expand each digit by place value: $6 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $3 \cdot 16^{0}$ . This gives $1, 763$ in base 10.

$\frac{1763}{10} = 176 r e m a \in d e r 3$

$\frac{176}{10} = 17 r e m a \in d e r 6$

$\frac{17}{10} = 1 r e m a \in d e r 7$

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

$3 \to 6 \to 7 \to 1 = 1763$

$1763 (b a s e 10) = {(1763)}_{10}$

Repeatedly divide $1, 763$ by $10$ , collect remainders, and read them in reverse to get $1, 763$ .

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