Math / Numbers & Operations

Question $33_{5}$ to base 2

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

STEP 3

Convert the base 5 number $33_5$ to base 10.
The base 5 number $33_5$ can be expanded as: $3 \times 5^1 + 3 \times 5^0$
Calculate each term: $3 \times 5^1 = 15$ $3 \times 5^0 = 3$
Add the results to get the base 10 equivalent: $15 + 3 = 18$
So, $33_5 = 18_{10}$ .

STEP 4

Convert the base 10 number $18_{10}$ to base 2.
Divide the number by 2 and record the remainders: $18 \div 2 = 9 \quad \text{remainder} = 0$ $9 \div 2 = 4 \quad \text{remainder} = 1$ $4 \div 2 = 2 \quad \text{remainder} = 0$ $2 \div 2 = 1 \quad \text{remainder} = 0$ $1 \div 2 = 0 \quad \text{remainder} = 1$
Read the remainders from bottom to top to get the base 2 equivalent: $10010_2$
The base 2 equivalent of $33_5$ is:
$\boxed{10010_2}$

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