Base Systems in Numbers

Base Systems in Numbers

A binary number system represents numbers that uses only two symbols, typically "0" (zero) and "1" (one).

Base 2

For writing numbers, the decimal system uses ten decimal digits. The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Base 10

Let's start with the basics.

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What is 101₂ in decimal?

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What is 13₁₀ in binary?

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What is 11111₂ in decimal?

Let's try something else

Decimals, fractions and negatives.

Fractions in binary arithmetic terminate only if 2 is the only prime factor in the denominator. As a result, 1/10 does not have a finite binary representation (10 has prime factors 2 and 5). This causes 10 × 1/10 not to precisely equal 1 in binary floating-point arithmetic.

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What is 0.1₂ in decimal

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What is 0.0666...₁₀ in binary?

Multiple Choice

True or False: 0.333...₁₀ is equal to 0.010101...₂.

• True
• False

Base 12

Using twelve as its base, various symbols have been used to stand for ten and eleven in duodecimal notation; we will use A and B, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10

Multiple Choice

Which number in decimal is equal to 2A3₁₂?

• 411
• 133
• 523
• 312

Multiple Select

Which numbers in dozenal are in the decimal thousands?

• 1060

• 700

• 40A

• 6B4

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What is -BB4;A₁₂ in decimal?

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What is 100,239.4₁₀ in dozenal?

Most common in YouTube links to videos.

Uses 0-9, A-Z, a-z, +, /. YouTube uses - and _ instead.

Base 64

Hexadecimal uses sixteen distinct symbols, most often the symbols 0-F instead of 0-B. You will easily get this, so we skip it for now.

Base 16

The first one here is similar.

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What is 17,002,095,308,465,627,000₁₀ in Base 64?

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What is UacpJLe2LAU₆₄ in decimal?

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What is owMTdAB8u1c₆₄ in decimal?