You are absolutely correct that many traits are not "digital", but "analog". In genetics, these are usually called quantitative traits. Such traits generally do not follow Mendel's laws of inheritance, but are said to have "complex inheritance". Most traits (phenotypes) in biology at the level of whole organisms probably have complex genetics; height is a classic example.
It is thought that complex traits arise by the combined actions of many genes (via their encoded proteins), while Mendelian inheritance occurs when phenotypes happen to correspond to the activity of a single gene. For very complex traits like height, many functions of the body might be involved, so the number of genes that may have some effect on the trait can be very large, but the effect of any single gene on the trait is likely small. In general, it is not understood exactly how genes contribute to the trait in such complex traits, so a phenomenological/statistical approach is used where the trait is modeled as some simple function of the genotype which is fit to data. Wikipedia's page on quantitative genetics has more information on this.
In addition, traits may of course be affected by environmental factors as well as genetics. Height for example is strongly affected by having access to good nutrition. See this article for some discussion.
For traits with complex genetics, the underlying genes are generally difficult to identify, and for along time we have known almost nothing about the genetics of traits like height, obesity and diabetes. Since the early 2000's, massive efforts have been put into mapping the genetics of such complex traits by brute force --- measuring the effect of all genes on the trait in a very large number of individuals, in so-called genome-wide association studies. These have revealed a large number of genes over the past decade, but as expected each has only a small effect on the trait.