Solution - Base conversion

738

738

Step-by-step explanation

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

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

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

$2 \cdot 16^{2} + 14 \cdot 16^{1} + 2 \cdot 16^{0} = 738$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $2 \cdot 16^{0}$ . This gives $738$ in base 10.

$\frac{738}{10} = 73 r e m a \in d e r 8$

$\frac{73}{10} = 7 r e m a \in d e r 3$

$\frac{7}{10} = 0 r e m a \in d e r 7$

$8 \to 3 \to 7 = 738$

$738 (b a s e 10) = {(738)}_{10}$

Repeatedly divide $738$ by $10$ , collect remainders, and read them in reverse to get $738$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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