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elementary-math Module

Interactive Simulation Screen

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Lesson Directive // Binary NumbersREF_CORE

\text{Value}

=

\sum_{i=0}^{n}

b_i

\cdot

2^i

Hover over a variable in the formula above, or see glossary below:

b_i

Binary Digit (Bit)

0 or 1

Unlike our normal Base-10 system which uses digits 0-9, binary only uses 0 and 1. Each position represents a power of 2 instead of a power of 10.

INSIGHT: Computers use binary because it perfectly maps to electrical switches being OFF (0) or ON (1).

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Syllabus Worked Example

Q: Convert the binary number 1011_2 to decimal.

1.Write out the powers of 2 for each position from right to left: 2^3, 2^2, 2^1, 2^0

2.Multiply each bit by its corresponding power of 2: 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1

3.Add them up: 8 + 0 + 2 + 1 = 11

Result:1011_2 = 11_{10}