Hex to Binary Converter

Need the raw bits behind a hex value? The Hex to Binary Converter takes whatever you drop into the Hex Input field and expands every digit into its 4-bit binary group in the Binary Output box. You can paste multiple values (one per line) for a batch conversion, then use the grouped-digit option to make long strings easier to read before copying your result. If you're working with legacy Unix file permissions written in octal, the octal to decimal converter converts them straight to decimal for you.

What Is the Hexadecimal System? A Foundation for Hex to Binary Conversion

Hexadecimal System and Base-16 Notation

The hexadecimal system (hex, for short) uses 16 as its base, or radix. As a base-16 counting scheme, it draws on exactly 16 symbols to express any value: the 10 decimal digits (0 through 9) plus the letters A B C D E F, standing in for the values 10 through 15. Each position in a hex number represents a power of 16, so a three-digit hex number like 62C expands as:

$$62C_{16} = 6 \times 16^{2} + 2 \times 16^{1} + 12 \times 16^{0} = 1580_{10}$$

This positional scheme makes hex a compact way to write out the bit patterns machines actually store and process. Because each hex character maps perfectly onto exactly four binary digits (a nibble), it acts as human-friendly shorthand for binary — the hexadecimal to binary conversion chart below shows this one-to-one correspondence for every hex digit.

In web development, colors are expressed as a 6-digit hex code: #ffffff represents white (binary 11111111 11111111 11111111), while #000000 represents black (three groups of 00000000). Every time you inspect a color value or a memory address in a hex editor, you're working with this base-16 scheme.

Valid Hexadecimal Characters: 0–9 and A–F

Valid hex characters are exclusively 0–9 and A–F (also written a–f in lowercase — this converter accepts either case). The table below shows every hex digit alongside its decimal value and its 4-bit binary nibble — the foundation of every hex-to-binary conversion:

Hexadecimal	Decimal	Binary (Nibble)
0	0	`0000`
1	1	`0001`
2	2	`0010`
3	3	`0011`
4	4	`0100`
5	5	`0101`
6	6	`0110`
7	7	`0111`
8	8	`1000`
9	9	`1001`
A	10	`1010`
B	11	`1011`
C	12	`1100`
D	13	`1101`
E	14	`1110`
F	15	`1111`

Notice how the lowest digit (0) maps to 0000 and the highest single hex character (F) maps to 1111 — all four bit positions set. This one-to-one correspondence between a hex symbol and a 4-bit group is exactly why hex is such a useful shorthand for binary in microcontroller work, networking, and hardware register documentation.

Infographic showing how to convert hexadecimal 3D9 to binary: convert each hex digit to its own 4-bit binary group, then combine the groups to get 0011 1101 1001 — Hex to Binary Converter: 3D9 = 0011 1101 1001

Understanding the Binary Numeral System

How Binary Represents Data in Computers

The binary numeral system uses 2 as its base (radix), giving it exactly 2 symbols: zero and one. Every binary digit — a bit — physically corresponds to an electrical signal in an on state (1) or off state (0) inside a circuit. This makes binary the native language of every digital system, from a single transistor up to the text rendering on your screen right now. Because every position in a binary number represents a power of 2, the value of any binary number is the sum of those powers:

$$1101_{2} = 1 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 13_{10}$$

The rightmost position holds 2 to the power of 0 (value 1), then moving left gives 2¹ (2), 2² (4), and 2³ (8) — the familiar 8-4-2-1 weights used in every nibble-level hex-to-binary conversion. These weights are the key to reading any binary result this converter produces.

Binary Grouping and the Nibble

In the base-2 counting scheme, bits are grouped into practical structures. A nibble is exactly four binary digits — half an octet (byte). Two nibbles make one octet (8 positions), covering the decimal range 0–255. In hex, that same range is just two characters instead of eight binary digits — which is the whole reason hex exists as a notation.

How to Convert Hex to Binary — Step-by-Step Manual Method

The 8-4-2-1 Weight Method

Converting hex to binary by hand is one of the most direct base-conversion operations, because the two systems align perfectly: every hex character always expands to exactly four binary digits, with no remainders to carry between characters. Here's the complete process for a hex value of any length:

Step 1 — Write out each hex character individually: Separate your hex input into its symbols. For letters A–F, note their decimal equivalents (A=10, B=11, C=12, D=13, E=14, F=15). For 4FA: the digits are 4, F, A → decimal values 4, 15, 10.
Step 2 — Write the 8-4-2-1 weights below each character: Every hex symbol expands into four positions with weights 8, 4, 2, and 1 (left to right).
Step 3 — Determine which weights sum to each decimal value: For digit 4: only the 4-weight is used → 0100. For digit F (15): 8+4+2+1=15, so all four are used → 1111. For digit A (10): 8+2=10 → 1010.
Step 4 — Concatenate the groups left to right to form the full binary output.

Worked Examples: Hex to Binary with Full Nibble Grids

Example 1 — Single byte: 4F

Hex digit :  4        F
Decimal   :  4       15
Weights   : 8421    8421
Bits      : 0100    1111

Result: 4F₁₆ = 0100 1111₂ — decimal 79.

Example 2 — Three-character hex: 4FA

Hex digit :  4        F        A
Decimal   :  4       15       10
Weights   : 8421    8421    8421
Bits      : 0100    1111    1010

Concatenating the groups gives 0100 1111 1010₂. The leading zero in the first group is preserved when you want a byte-aligned binary output, or can be dropped for the shortest correct representation.

Example 3 — Four-character hex: 9DB2

Hex digit :  9        D        B        2
Decimal   :  9       13       11        2
Weights   : 8421    8421    8421    8421
Bits      : 1001    1101    1011    0010

Result: 9DB2₁₆ = 1001 1101 1011 0010₂ — a 16-bit binary result, exactly the kind of output you'd need when inspecting a hex bitmask or checking which bits are set inside a processor register.

A longer example: the hex string 48656C6C6F (the word "Hello" as ASCII hex) expands to:

48 → 01001000
65 → 01100101
6C → 01101100
6C → 01101100
6F → 01101111

This demonstrates how the same group-by-group logic scales to any length of hex string, one nibble per character.

Using the Hex to Binary Converter

Input, Output, and the Group Digits Option

This hex to binary converter is a free, browser-based tool that converts as you type — there's no separate "run" step required, though a Convert button is there too if you prefer to trigger it manually. Here's how to get the most from it:

Enter your value: Type or paste your hex value into the Hex Input box. Uppercase and lowercase hex characters both work (1a3f and 1A3F are equally valid). Spaces between characters are ignored automatically.
Convert multiple values at once: Put each hex value on its own line and every line converts independently, in order — useful for checking a whole list of register values in one pass.
Group digits for readability: Toggle the Group digits option to break a long binary output into nibble- or byte-sized chunks instead of one unbroken string, which makes long results easier to read before copying.
Copy the result: Use the Copy button next to the Binary Output box to grab the result for use in code, documentation, or a homework write-up.
Start over: Use the Clear button to reset both the input and output fields.

If you enter an invalid character — anything outside 0–9 and A–F — the converter shows a clear error message identifying which line is invalid, rather than silently producing a partial or wrong result.

Why Convert Hex to Binary? Real-World Use Cases

Practical Reasons to Reach for a Hex to Binary Converter

Register and memory-dump inspection: When a CPU register or storage dump shows a hex value, converting it to binary lets you inspect individual bit positions — seeing at a glance which flags are set or clear inside a hex bitmask.
Bitwise operations in low-level coding: Engineers writing C, assembly, or any language that exposes AND/OR/XOR/shift operators often reason more easily in binary than in hex when checking the exact bits an operation touches.
Networking and protocol analysis: IP addresses, subnet masks, and packet headers are frequently displayed in hex. Expanding to binary reveals the exact bit structure behind CIDR notation and header flags.
Circuit design and microcontroller work: Hardware datasheets specify register values in hex; converting to binary shows exactly which pin states, interrupt flags, or peripheral configuration bits are active.
Education and coursework: A dependable free tool for computer science and digital logic courses — no account, no install, and results that update as you type, which makes checking base-conversion homework fast.

Privacy and Related Hex Conversion Tools

All conversion happens entirely in your browser — nothing you type is transmitted to a server, stored, or logged. There's no account required and no tracking, which matters if you're working with values pulled from proprietary firmware or a sensitive memory dump.

Whether you're inspecting a hex register bit by bit, building intuition for binary representation in a computer science course, or working through a hardware datasheet at the signal level, this hex to binary converter — and its family of related conversion tools — gives you instant, accurate, and private results for any hex input, from a single character to a long multi-line batch.