Bash Script to Convert Decimal to Binary Number

Use a Bash script with a loop and bitwise operations like while [ $decimal -gt 0 ]; do binary=$((decimal % 2))$binary; decimal=$((decimal / 2)); done to convert decimal to binary.

Examples

Input0

Output0

Input5

Output101

Input18

Output10010

How to Think About It

To convert decimal to binary, repeatedly divide the decimal number by 2 and record the remainder each time. These remainders, read in reverse order, form the binary number. Stop when the decimal number becomes zero.

Algorithm

1

Get the decimal input number

2

If the number is zero, return 0

3

While the number is greater than zero:

4

Find remainder of number divided by 2

5

Prepend remainder to the binary result string

6

Divide the number by 2 (integer division)

7

Return the binary result string

Code

bash

#!/bin/bash
read -p "Enter a decimal number: " decimal
if [ "$decimal" -eq 0 ]; then
  echo 0
  exit
fi
binary=""
while [ $decimal -gt 0 ]; do
  remainder=$((decimal % 2))
  binary="$remainder$binary"
  decimal=$((decimal / 2))
done
echo "$binary"

Output

Enter a decimal number: 18
10010

Dry Run

Let's trace the decimal number 5 through the code

1

Initial input

decimal = 5, binary = ""

2

First loop iteration

remainder = 5 % 2 = 1, binary = "1", decimal = 5 / 2 = 2

3

Second loop iteration

remainder = 2 % 2 = 0, binary = "01", decimal = 2 / 2 = 1

4

Third loop iteration

remainder = 1 % 2 = 1, binary = "101", decimal = 1 / 2 = 0

5

Loop ends

decimal = 0, final binary = "101"

decimal	remainder	binary
5	1	1
2	0	01
1	1	101

Why This Works

Step 1: Divide and get remainder

Each division by 2 gives a remainder of 0 or 1, which is a binary digit.

Step 2: Build binary string

Prepending the remainder builds the binary number from least significant bit to most.

Step 3: Stop when zero

When the decimal number reaches zero, all binary digits are collected.

Alternative Approaches

Using printf with built-in conversion

bash

read -p "Enter decimal: " decimal
printf "%b\n" "$(echo "obase=2; $decimal" | bc)"

Uses external bc command for conversion; simpler but requires bc installed.

Using Bash built-in printf with %d and %b

bash

read -p "Enter decimal: " decimal
printf '%d in binary is %s\n' "$decimal" "$(echo "obase=2; $decimal" | bc)"

Combines input and output formatting; still depends on bc.

Complexity: O(log n) time, O(log n) space

Time Complexity

The loop runs once for each binary digit, which is proportional to log base 2 of the decimal number.

Space Complexity

The binary string grows with the number of bits, so space is proportional to log base 2 of the input.

Which Approach is Fastest?

The manual loop is efficient and requires no external tools; using bc is simpler but depends on external command.

Approach	Time	Space	Best For
Manual loop with division	O(log n)	O(log n)	No dependencies, educational
Using bc command	O(log n)	O(log n)	Quick and simple if bc is available