Solution - Base conversion

1, 252

1,252

Step-by-step explanation

${(4 E 4)}_{16} = b a s e 10$

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

${(4 E 4)}_{16} = 4 \cdot 16^{2} + 14 \cdot 16^{1} + 4 \cdot 16^{0}$

$4 \cdot 16^{2} + 14 \cdot 16^{1} + 4 \cdot 16^{0} = 1252$

Expand each digit by place value: $4 \cdot 16^{2}$
+ $14 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $1, 252$ in base 10.

$\frac{1252}{10} = 125 r e m a \in d e r 2$

$\frac{125}{10} = 12 r e m a \in d e r 5$

$\frac{12}{10} = 1 r e m a \in d e r 2$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$2 \to 5 \to 2 \to 1 = 1252$

$1252 (b a s e 10) = {(1252)}_{10}$

Repeatedly divide $1, 252$ by $10$ , collect remainders, and read them in reverse to get $1, 252$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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