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tokens: magnitudes using the parsec isochrones. We then pair the single stars to make binaries assuming a non-random pairing of the binary components. According to the hydrodynamical simulations of star cluster formation by Bate ( 2009 ), the multiplicity fraction is approximately proportional to the logarithm of the primary mass. As a result, we assume that the probability that a single star with mass m prim is the primary component of a binary, scales linearly with the logarithm of its mass, i.e. Prob ∝ log 10 ( m prim ). We also assume a flat distribution function for the mass ratio 0 ≤ q ≤ 1.0. We then calculate the total J and K s magnitudes of each binary from the sum of the luminosities of its components. We also add photometric errors to the magnitudes of single and binary stars. The photometric errors resemble the photometric errors of PPMXL at each magnitude. Using this procedure, we make a synthetic CMD of a cluster with single stars and binary systems. We then apply our photometric membership criterion (Section 4.2 ) on this synthetic CMD through a blind test and count the number of single stars and binaries. Photometrically, a single star is any point that lies within 2.5σ of the isochrone and a binary is any non-single star whose vertical deviation from the isochrone is less than 0.75 mag. Finally, we change the low-mass and the high-mass slopes of the MF (α low , α high ) in ranges (0.70, 1.25) and (2.00, 2.60), respectively, until we find the best match with the observed MF (using K-S test) and the observed binary fraction. For each set of the simulation parameters, we have simulated 40 clusters with different random seed numbers, to reduce the errors caused by statistical fluctuations. Fig. 8 , shows the synthetic CMD of one of our simulated clusters (left-hand panel) and the detected single stars and binaries after applying the blind photometric test. In this figure, the true binary fraction is 23 per cent in the mass range 0.10 ≤ M / M ⊙ ≤ 4.68, but the observed binary fraction is only ∼6 per cent. Figure 8. (Left) Synthetic CMDs of simulated binaries (red filled circles) and single stars (black open squares) for a true binary fraction of 23 per cent over the whole mass range (0.1 m / M ⊙ 4.68). The scatter of single stars is due to the added photometric errors which resemble actual photometric errors in PPMXL. (Right) The detected binaries (red filled circles) as well as single stars (blue filled circles) after applying the blind photometric test on the simulated data. As it can be seen, many of the binaries have been identified as single stars. The observed binary fraction is ∼6 per cent. The parsec isochrone which is used in the blind photometric test, is shown by the black solid line. Table 4 compares the binary fractions of Alpha Persei from different studies. According to the outcome of our Monte Carlo simulations, the binary fraction of the cluster over the mass range 0.70 m / M ⊙ 4.68 is 34 ± 12 per cent, in agreement with