Solution - Base conversion

931

931

Step-by-step explanation

${(3 A 3)}_{16} = b a s e 10$

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

${(3 A 3)}_{16} = 3 \cdot 16^{2} + 10 \cdot 16^{1} + 3 \cdot 16^{0}$

$3 \cdot 16^{2} + 10 \cdot 16^{1} + 3 \cdot 16^{0} = 931$

Expand each digit by place value: $3 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $3 \cdot 16^{0}$ . This gives $931$ in base 10.

$\frac{931}{10} = 93 r e m a \in d e r 1$

$\frac{93}{10} = 9 r e m a \in d e r 3$

$\frac{9}{10} = 0 r e m a \in d e r 9$

$1 \to 3 \to 9 = 931$

$931 (b a s e 10) = {(931)}_{10}$

Repeatedly divide $931$ by $10$ , collect remainders, and read them in reverse to get $931$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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