In daviddoret/haricot: Algorithm Composition, Manipulation And Analysis

knitr::opts_chunk$set(echo = TRUE)

Definition

In the context of the haricot package, two modular binary numbers are equal if and only if they have identical dimensions and all their corresponding bits are equal.

Formal definition

$$\forall B_{a},B_{b} \in \mathbb{B}^{d}, B_{a} = B_{b} \Leftrightarrow \forall i \in [1,...,d], B_{a}[i] = B_{b}[i]$$ It follows from this definition that if two modular binary numbers are equal, they are iso-dimensional.

$$ \forall B_{a},B_{b} \in \mathbb{B}, B_{a} = B_{b} \Leftrightarrow , dim(B_{a}) = dim(B_{b}) $$

Inequality of modular binary numbers for equal mapped integers

A consequence of this definition of equality is that 2 modular binary numbers may be unequal but be mapped to the same natural number.

$$\forall B_{a},B_{b} \in \mathbb{B}, int(B_{a}) = int(B_{b}) \nRightarrow B_{a} = B_{b}$$

Example:

$$b0000 \neq b00 \land int(b0000) = int(b00)$$

Inequality

TODO: COMPLETE HERE

See also

• Modular binary number

daviddoret/haricot documentation built on May 21, 2019, 1:42 a.m.