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.

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.

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

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.