Number Base Conversions

Explore different number base conversions with interactive cards. Flip each card to see examples and more details.

Formula:Decimal = ∑(bi × 2^i)

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Binary to Decimal

Convert binary 1011 to decimal:

1011₂ = (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)
       = 8 + 0 + 2 + 1
       = 11₁₀

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Formula:Divide by 2 and record remainders

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Convert decimal 13 to binary:

13 ÷ 2 = 6, remainder 1
 6 ÷ 2 = 3, remainder 0
 3 ÷ 2 = 1, remainder 1
 1 ÷ 2 = 0, remainder 1

Binary = 1101

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Formula:Group into 4-bit sets and convert

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Convert binary 11010110 to hexadecimal:

Group into 4-bit groups: 1101 0110
Convert each group:
 1101 = D
 0110 = 6

Hexadecimal = D6

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Formula:Convert each hex digit to 4-bit binary

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Convert hexadecimal 2F to binary:

2 = 0010
F = 1111

Binary = 00101111

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Formula:Group into 3-bit sets and convert

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Convert binary 110101 to octal:

Group into 3-bit groups: 110 101
Convert each group:
 110 = 6
 101 = 5

Octal = 65

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Formula:Convert each octal digit to 3-bit binary

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Convert octal 47 to binary:

4 = 100
7 = 111

Binary = 100111

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