Solution - Base conversion

742

742

Step-by-step explanation

${(2 E 6)}_{16} = b a s e 10$

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

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

$2 \cdot 16^{2} + 14 \cdot 16^{1} + 6 \cdot 16^{0} = 742$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $6 \cdot 16^{0}$ . This gives $742$ in base 10.

$\frac{742}{10} = 74 r e m a \in d e r 2$

$\frac{74}{10} = 7 r e m a \in d e r 4$

$\frac{7}{10} = 0 r e m a \in d e r 7$

$2 \to 4 \to 7 = 742$

$742 (b a s e 10) = {(742)}_{10}$

Repeatedly divide $742$ by $10$ , collect remainders, and read them in reverse to get $742$ .

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