Solution - Base conversion

697

697

Step-by-step explanation

${(2 B 9)}_{16} = b a s e 10$

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

${(2 B 9)}_{16} = 2 \cdot 16^{2} + 11 \cdot 16^{1} + 9 \cdot 16^{0}$

$2 \cdot 16^{2} + 11 \cdot 16^{1} + 9 \cdot 16^{0} = 697$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $11 \cdot 16^{1}$
+ $9 \cdot 16^{0}$ . This gives $697$ in base 10.

$\frac{697}{10} = 69 r e m a \in d e r 7$

$\frac{69}{10} = 6 r e m a \in d e r 9$

$\frac{6}{10} = 0 r e m a \in d e r 6$

$7 \to 9 \to 6 = 697$

$697 (b a s e 10) = {(697)}_{10}$

Repeatedly divide $697$ by $10$ , collect remainders, and read them in reverse to get $697$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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