Algebra Examples

$1011_{2}$

Step 1

Multiply each digit of $1011$ by a power of $2$ . Starting from the right, it will be $2^{0}$ . Add these terms together.

$1 \cdot 2^{3} + 0 \cdot 2^{2} + 1 \cdot 2^{1} + 1 \cdot 2^{0}$

Step 2

Multiply and add terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2^{3}$ by $1$ .

$2^{3} + 0 \cdot 2^{2} + 1 \cdot 2^{1} + 1 \cdot 2^{0}$

Step 2.1.2

Raise $2$ to the power of $3$ .

$8 + 0 \cdot 2^{2} + 1 \cdot 2^{1} + 1 \cdot 2^{0}$

Step 2.1.3

Raise $2$ to the power of $2$ .

$8 + 0 \cdot 4 + 1 \cdot 2^{1} + 1 \cdot 2^{0}$

Step 2.1.4

Multiply $0$ by $4$ .

$8 + 0 + 1 \cdot 2^{1} + 1 \cdot 2^{0}$

Step 2.1.5

Multiply $2^{1}$ by $1$ .

$8 + 0 + 2^{1} + 1 \cdot 2^{0}$

Step 2.1.6

Evaluate the exponent.

$8 + 0 + 2 + 1 \cdot 2^{0}$

Step 2.1.7

Multiply $2^{0}$ by $1$ .

$8 + 0 + 2 + 2^{0}$

Step 2.1.8

Anything raised to $0$ is $1$ .

$8 + 0 + 2 + 1$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $8$ and $0$ .

$8 + 2 + 1$

Step 2.2.2

Add $8$ and $2$ .

$10 + 1$

Step 2.2.3

Add $10$ and $1$ .

$11$