I am not sure whether your question is about the creation of a data.frame
object with several types of variables (see comment) or how to compute correlations if your data is, as you mentioned, "numerical and binary" (*). This link might help. I assume in particular Dan Chaltiel's answer (last answer) will help you.
(*) In the letter case the thread is possibly a duplicate.
EDIT: Considering Dan Chaltiel's approach (see link), does this help?
df <- data.frame(a=c(34,54,55,12,13,6),
b=c("FALSE","TRUE","TRUE","TRUE","TRUE","FALSE"),
c=c(1:6))
library(dplyr)
model.matrix(~0+., data=df) %>%
cor(use="pairwise.complete.obs")