Reverse Binary Numbers

What Is Binary Reversal / Bit Reversal?

Binary reversal is the process of mirror-inverting the sequence of digits in a binary representation. For a given binary number, its index values are reversed from left-to-right (the most significant bit becomes the least significant bit and vice versa). Bit reversal permutations are highly significant in discrete digital signal processing (DSP) and sorting algorithms.

How Bit Reversal Works

To reverse the bits of a binary sequence, start from the last digit and write the sequence backwards towards the first digit.

Example:

Binary value: 1101 (decimal 13) reversed is 1011 (decimal 11).
Binary value: 11110000 (decimal 240) reversed is 00001111 (decimal 15).
Binary value: 10000000 (decimal 128) reversed is 00000001 (decimal 1).

Applications of Bit Reversal

Cooley-Tukey FFT Algorithm: The Fast Fourier Transform (FFT) requires inputs to be reordered using bit-reversal permutations. This reordering is necessary because the algorithm breaks down calculations in a recursive structure, resulting in output values in bit-reversed order.
Data Scrambling: Used in specialized hardware configurations to scramble address lines for randomizing read/write speeds or distributing storage cells.

Frequently Asked Questions

Does bit reversal change the numerical value?

Yes, in almost all cases. Since reversing the bits changes which place-values (powers of two) are active, the decimal equivalent changes significantly. For instance, 1100 (12) becomes 0011 (3).

What does the "Reverse List / Line Order" checkbox do?

By default, the tool reverses the bit sequence of each individual binary number but keeps the vertical line order intact. Checking this box will *also* reverse the vertical order of the lines (first input becomes the last output line, etc.), giving complete reversal.

Can I process hex or decimal values?

This tool is dedicated strictly to binary strings. You can use our other tools (such as Decimal to Binary or Hex to Binary) to convert your values, then paste the results here to execute the reversal.

Does the tool handle prefixes like 0b?

Yes. Standard programming prefixes like 0b or 0B are ignored during bit reversal and can be optionally restored to the output using the "Add 0b Prefix to Result" toggle.