Times-tables and more

Tables of various numerical “binary operations” (i.e. ways of combining two numbers into another number). This includes the usual “times tables” taught by most schools, but also some simpler ones (e.g. addition, maximum, minimum) and some more advanced (e.g. quadrance, harmonic mean, bitwise XOR, etc.). Useful for printing out and colouring in, to spot patterns.

The HTML pages are coloured according the RdBu colour map: zero is white, positive values get increasingly blue and negative values get increasingly red (based on the range of values within the table). These are background colours, so the “include background” option provided in the print dialog of browsers (e.g. Firefox) can be used to toggle them on/off.

Tables

Beginner

These are very simple, and may be useful for learning how to read these tables:

1ˢᵗ

This table tabulates the operation which returns its first argument unchanged. Algebraically, we can define that function as:

1ˢᵗ(x, y) = x

The table has horizontal stripes of equal values, showing that we are using the row number as the first argument, i.e. the rows correspond to x in these equations. This is useful for understanding how to read all of these tables.

This operation is associative and idempotent. It is dual to 2ⁿᵈ.

2ⁿᵈ

This table tabulates the operation dual to that of 1ˢᵗ. It

Minimum

Maximum

Basic arithmetic

Addition

Subtraction

Multiplication

Division

Quotient

Modulo

Advanced arithmetic

Least common multiple

Greatest common divisor

Exponential

Logarithm

Mean

Harmonic mean

Logarithmic mean

LogSumExp

Geometry

Euclidean quadrance

Relativistic quadrance

Bitwise

AND

Inclusive OR

Exclusive OR