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We prove that for every positive integer $m$, there exist infinitely manysimple abelian varieties over $\mathbb{F}_2$ of order $m$. The method isconstructive, building on the work of Madan--Pal in the case $m=1$ to producean explicit sequence of Weil polynomials giving rise to abelian varieties over$\mathbb{F}_2$ of order $m$. This sequence itself depends on the choice of asuitable generalized binary representation of $m$; by making careful choices ofthis representation, we can ensure that the the resulting sequence ofpolynomials have 2-adic Newton polygons which guarantee the existence ofsuitable irreducible factors.

Abelian varieties over $\mathbb{F}_2$ of prescribed order