Generating random uniform random numbers from coin flip algorithm tends to generate more 0s than expected

I am trying to generate random numbers in the range from 0 to 99 using a function rcoin that returns 0 or 1 with equal probability. I have written the following code that converts a binary number generated from successive calls of rcoin function, and then returns it with the condition that the number is less than 100. Here is the R code.

rcoin <- function() {
  rbinom(n = 1, size = 1, prob = 0.5)
}

r100 <- function(n=100) {
  v = n + 1
  while(v > n) {
    v = sum(sapply(0:6, function(i) rcoin() * 2 ^ i))
  }
  v
}

val_plot <- function() {
  N = 10000
  rand_sample <- rep(0, N)
  for (i in 1:N){
    rand_sample[i] = r100()
  }
  hist(rand_sample, breaks = 100)
}

val_plot() 

It is supposed to produce uniform random numbers from 0 to 99, as truncated uniform distribution is also uniform. But when I plot the histogram of 10000 generated values, I see the value 0 is generated for unusually large number of times, but all other values follow a uniform distribution. Why? I guess this is because the binary number "1111111" is getting rejected whereas "0000000" is not. But how do I solve this issue? Is there any way to improve it?