Math / Numbers & Operations

Question335 to base? $313$

Studdy Solution

STEP 1

1. The number $33_5$ is in base 5.
2. We need to convert this number to base 2.

STEP 2

1. Convert the number from base 5 to base 10.
2. Convert the number from base 10 to base 2.

STEP 3

Express the base 5 number $33_5$ in terms of base 10.
$33_5 = 3 \times 5^1 + 3 \times 5^0$

STEP 4

Calculate the powers of 5 and multiply by the respective coefficients.
$3 \times 5^1 = 3 \times 5 = 15$ $3 \times 5^0 = 3 \times 1 = 3$

STEP 5

Add the results to get the base 10 equivalent.
$15 + 3 = 18$

STEP 6

Convert the base 10 number $18$ to base 2 by dividing by 2 and recording the remainders.
$18 \div 2 = 9 \quad \text{remainder} \, 0$ $9 \div 2 = 4 \quad \text{remainder} \, 1$ $4 \div 2 = 2 \quad \text{remainder} \, 0$ $2 \div 2 = 1 \quad \text{remainder} \, 0$ $1 \div 2 = 0 \quad \text{remainder} \, 1$

STEP 7

Write the remainders in reverse order to get the base 2 number.
The base 2 equivalent of $18_{10}$ is $10010_2$ .
The base 2 equivalent of $33_5$ is:
$\boxed{10010_2}$

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