Shift of Base

This page is a sub-page of our page on Numbers.

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Related KMR pages:

• Numbers and their Digits in different Bases.
Representation and Reconstruction of Numbers.
Shift of Basis (in general).

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Other sources of related information:

Number systems

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Experiment here with computing the Digits of a Number with respect to different Bases.

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The Base-Shift formula for Numbers

It is often useful to have a symbolic name for the operation of shifting the \, B_{ase} \, of a \, n_{umber} \, from \, {B_{ase}}_1 \, to \, {B_{ase}}_2 \,. This operation will be called \, B_{aseShift} \, and its action on a given \, n_{umber} \, will be written in three different ways:

i) \, {[B_{aseShift}]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , or

ii) \, {[n_{umber}]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , if the \, B_{aseShift} \, operation is clear from the context, or

iii) \, {[\,\,\,]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , if both the \, n_{umber} \, and the \, B_{aseShift} \, operation are clear from the context.

A Base-Shift Diagram for Numbers:
A Base-Shift diagram for Numbers

Numbers are naturally related to Music:

Numbers  are Naturally Related to Music

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