Solution - Base conversion

502

502

Step-by-step explanation

${(1 F 6)}_{16} = b a s e 10$

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

${(1 F 6)}_{16} = 1 \cdot 16^{2} + 15 \cdot 16^{1} + 6 \cdot 16^{0}$

$1 \cdot 16^{2} + 15 \cdot 16^{1} + 6 \cdot 16^{0} = 502$

Expand each digit by place value: $1 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $6 \cdot 16^{0}$ . This gives $502$ in base 10.

$\frac{502}{10} = 50 r e m a \in d e r 2$

$\frac{50}{10} = 5 r e m a \in d e r 0$

$\frac{5}{10} = 0 r e m a \in d e r 5$

$2 \to 0 \to 5 = 502$

$502 (b a s e 10) = {(502)}_{10}$

Repeatedly divide $502$ by $10$ , collect remainders, and read them in reverse to get $502$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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