Solution - Base conversion

2, 779

2,779

Step-by-step explanation

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

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

${(A D B)}_{16} = 10 \cdot 16^{2} + 13 \cdot 16^{1} + 11 \cdot 16^{0}$

$10 \cdot 16^{2} + 13 \cdot 16^{1} + 11 \cdot 16^{0} = 2779$

Expand each digit by place value: $10 \cdot 16^{2}$
+ $13 \cdot 16^{1}$
+ $11 \cdot 16^{0}$ . This gives $2, 779$ in base 10.

$\frac{2779}{10} = 277 r e m a \in d e r 9$

$\frac{277}{10} = 27 r e m a \in d e r 7$

$\frac{27}{10} = 2 r e m a \in d e r 7$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$9 \to 7 \to 7 \to 2 = 2779$

$2779 (b a s e 10) = {(2779)}_{10}$

Repeatedly divide $2, 779$ by $10$ , collect remainders, and read them in reverse to get $2, 779$ .

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