Decimal to Binary Conversion in R – Loop, Recursion, Vector Logic & Built-in

Learn how to convert decimal numbers to binary in R using four different techniques, each demonstrating a new way of thinking in R's syntax and logic style.

Where It’s Useful

• Data science tasks where binary encoding is required

• Learning base conversion logic in R

• Teaching number systems in programming education

• Writing utility functions for numeric preprocessing

Binary Conversion Using While Loop

# Convert decimal to binary using a basic while loop
decimal_to_binary_loop <- function(num) {
  if (num == 0) return("0")
  binary <- ""
  while (num > 0) {
    binary <- paste0(num %% 2, binary)
    num <- num %/% 2
  }
  return(binary)
}

cat("Binary of 19:", decimal_to_binary_loop(19), "\n")

How It Works

• %/% divides the number and drops decimals (integer division)

• %% gives the remainder

• Use paste0() to build the binary string by prepending digits

Output

Recursive Binary Conversion

# Convert decimal to binary using recursion
decimal_to_binary_recursive <- function(num) {
  if (num == 0) return("")
  return(paste0(decimal_to_binary_recursive(num %/% 2), num %% 2))
}

binary <- decimal_to_binary_recursive(23)
cat("Binary of 23:", ifelse(nchar(binary) == 0, "0", binary), "\n")

How It Works

• Function calls itself with the number divided by 2.

• On return, appends the remainder (num %% 2).

• Special handling for 0 with ifelse().

Output

Vector-Based Conversion Logic

# Convert decimal to binary using vectorized logic
decimal_to_binary_vector <- function(num) {
  if (num == 0) return("0")
  bits <- c()
  while (num > 0) {
    bits <- c(num %% 2, bits)
    num <- num %/% 2
  }
  return(paste(bits, collapse = ""))
}

cat("Binary of 30:", decimal_to_binary_vector(30), "\n")

How It Works

• Creates a vector bits and prepends each binary digit.

• paste(..., collapse = "") joins the vector into a string.

Output

Built-in Conversion using intToBits()

# Using intToBits() to get binary and trimming unused zeros
decimal_to_binary_builtin <- function(num) {
  bits <- intToBits(num)[1:32]
  binary <- paste(rev(as.integer(bits)), collapse = "")
  binary_trimmed <- sub("^0+", "", binary)  # remove leading zeros
  return(ifelse(nchar(binary_trimmed) == 0, "0", binary_trimmed))
}

cat("Binary of 10:", decimal_to_binary_builtin(10), "\n")

How It Works

• intToBits() returns a raw bit array (32 bits).

• Convert each bit to integer and reverse.

• Trim leading zeros using sub().

Output

Summary

You’ve just learned four powerful and clean ways to convert decimal numbers into binary using R. Each method — from classic loops and recursion to vector manipulation and intToBits() — offers a new angle to understand how binary conversion works in a statistical programming language like R.