Solution - Base conversion

3, 757

3,757

Step-by-step explanation

${(E A D)}_{16} = b a s e 10$

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

${(E A D)}_{16} = 14 \cdot 16^{2} + 10 \cdot 16^{1} + 13 \cdot 16^{0}$

$14 \cdot 16^{2} + 10 \cdot 16^{1} + 13 \cdot 16^{0} = 3757$

Expand each digit by place value: $14 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $13 \cdot 16^{0}$ . This gives $3, 757$ in base 10.

$\frac{3757}{10} = 375 r e m a \in d e r 7$

$\frac{375}{10} = 37 r e m a \in d e r 5$

$\frac{37}{10} = 3 r e m a \in d e r 7$

$\frac{3}{10} = 0 r e m a \in d e r 3$

$7 \to 5 \to 7 \to 3 = 3757$

$3757 (b a s e 10) = {(3757)}_{10}$

Repeatedly divide $3, 757$ by $10$ , collect remainders, and read them in reverse to get $3, 757$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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