This work explores the binarization of the deconvolution-based generator in a GAN for memory saving and speedup of image construction. Our study suggests that different from convolutional neural networks (including the discriminator) where all layers can be binarized, only some of the layers in the generator can be binarized without significant performance loss. Supported by theoretical analysis and verified by experiments, a direct metric based on the dimension of deconvolution operations is established, which can be used to quickly decide which layers in the generator can be binarized. Our results also indicate that both the generator and the discriminator should be binarized simultaneously for balanced competition and better performance. Experimental results based on CelebA suggest that directly applying state-of-the-art binarization techniques to all the layers of the generator will lead to 2.83$\times$ performance loss measured by sliced Wasserstein distance compared with the original generator, while applying them to selected layers only can yield up to 25.81$\times$ saving in memory consumption, and 1.96$\times$ and 1.32$\times$ speedup in inference and training respectively with little performance loss.