utility calculator

Binary, Hexadecimal, & ASCII Multi-Base Converter

Convert integers and strings between binary, hexadecimal, ASCII, and decimal formats instantly with this free online conversion tool.

Formula Verified by Dr. Arthur Pendelton, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Source Format

Input Value

Results

Plain Text representation

Hello

Binary Bitstream

01001000 01100101 01101100 01101100 01101111

Hexadecimal Bytes

48 65 6C 6C 6F

Decimal Bytes

72, 101, 108, 108, 111

Tip

Save this calculator to debug byte arrays, verify binary-to-hex encodings, and translate ASCII characters during programming tasks.

Formula

Positional Number System Conversions

Binary: base 2 (0-1) 
Hex: base 16 (0-9, A-F) 
Decimal: base 10 (0-9) 
ASCII: Character standard 0-127 mapping

Uses division-remainder radix conversion algorithms and TextEncoder character maps to translate representations.

Step by step

How the calculation works

1Select your input format: Plain Text, Binary stream, Hex bytes, or Decimal byte array.
2Type or paste your content in the input field.
3View real-time representations across all base systems and ASCII encodings.

Related guides

Learn more about this calculation

Guide

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Learn the fastest reliable workflow for using Do The Calculation calculators, reading results, checking formulas, and using save, print, share, and export actions correctly.

How to understand and use this calculator

Numeric Base Mathematics: Positional Representation and Base Conversions

Every number system uses positional notation where the value of a digit depends on its position relative to the radix (base). Binary is a base-2 system using digits {0, 1}, decimal is base-10 using {0..9}, and hexadecimal is base-16 using {0..9, A..F}.

To convert a decimal integer to binary or hexadecimal, we use the division-remainder method. The decimal number is repeatedly divided by the target base, and the remainders are recorded in reverse order. For example, to convert decimal 65 to binary: 65 / 2 = 32 R 1, 32 / 2 = 16 R 0, ..., reading the remainders upwards gives the binary representation `01000001`.

ASCII and Character Encoding: Representing Text in Binary Bytes

Computers cannot store letters directly; they can only store bits. To represent text, characters must be mapped to numbers using encoding standards. The American Standard Code for Information Interchange (ASCII) maps 128 characters to numbers from 0 to 127.

For example, the uppercase letter "A" is mapped to decimal 65. In binary, 65 is represented as the 8-bit byte `01000001`. In hexadecimal, 65 is represented as `41`. Modern systems build on this using UTF-8, which uses variable-length byte structures to encode millions of Unicode characters while remaining fully backward-compatible with ASCII.

Hexadecimal Notation: The Compact Representation of Binary Byte Structures

Binary code is difficult for humans to read and write. Hexadecimal provides a compact representation because one hexadecimal character corresponds to exactly four binary bits (a nibble). Since 2^4 = 16, any 8-bit byte can be written as exactly two hexadecimal characters.

For example, the binary string `11011011` can be split into two nibbles: `1101` (decimal 13, hex D) and `1011` (decimal 11, hex B), yielding the hexadecimal value `DB`. This direct mapping makes hexadecimal the standard format for representing memory addresses, color codes, and network MAC addresses.

Bitwise Operations and Hex/Binary Masks in Computer Systems

In computer systems, hexadecimal values are frequently used to define bitwise masks. A bitwise mask allows developers to isolate or modify specific bits within a byte using logical operations like AND, OR, and XOR. For example, a mask of `0x0F` (binary `00001111`) isolates the lower nibble of any byte.

To perform more complex base math, you can use our number base converter which supports bases 2 through 36, or translate binary streams to ASCII strings using the binary to text translator with a full bit-grid visualizer.

How to Use This Multi-Base Converter

Select the format of your input — Text, Binary, Hexadecimal, or Decimal — then type or paste the value. The calculator instantly shows the equivalent representation in all four formats: plain text, binary bitstream, hexadecimal bytes, and decimal byte values.

This is useful for debugging network packets, verifying character encodings, or converting between formats when working with low-level data.

Worked Example: Converting "Hello" Across All Four Formats

Starting from the text "Hello", the calculator encodes each character to its UTF-8 byte value: H=72, e=101, l=108, l=108, o=111.

These verified bytes translate to binary `01001000 01100101 01101100 01101100 01101111`, hexadecimal `48 65 6C 6C 6F`, and decimal `72, 101, 108, 108, 111` — all four views of the exact same 5-byte data.

Related Calculators

This converter is part of a Developer Tools cluster. For a text-only binary encoder/decoder, see the Binary to Text Translator. For other encoding formats, try the Base64 Text File Converter or the HTML Entities Encoder.

Related concepts

Radix (Base)

The number of unique digits, including zero, used to represent numbers in a positional numeral system.

Character Encoding

A set of rules that pairs each character from a repertoire with a unique numerical code.

Bitwise Mask

Data used in bitwise operations to select, set, clear, or toggle specific bits within a byte or word.

Frequently Asked Questions

What is binary?+

Binary is a base-2 numbering system that uses only two digits, 0 and 1, which represent the off and on states of electrical transistors in computer hardware.

What is hexadecimal?+

Hexadecimal is a base-16 numbering system that uses sixteen distinct symbols: 0–9 to represent values zero to nine, and A–F to represent values ten to fifteen.

What does ASCII stand for?+

ASCII stands for American Standard Code for Information Interchange, a character encoding standard for electronic communication.

How do you convert binary to hexadecimal?+

Group the binary bits into sets of four starting from the right. Convert each 4-bit group (nibble) into its equivalent hexadecimal digit (0–F).

Why is hexadecimal used in programming?+

Hexadecimal is used because it represents binary bytes in a compact, human-readable format. One byte (8 bits) can always be written as exactly two hex digits.

What is a nibble?+

A nibble is a four-bit aggregation, or half an octet (half a byte). It represents values from 0 to 15, corresponding to exactly one hexadecimal digit.

How do you represent a space in ASCII?+

A space character is represented by decimal value 32 in the ASCII table, which corresponds to binary 00100000 and hexadecimal 20.

What is the difference between ASCII and Unicode?+

ASCII is a 7-bit encoding representing 128 English characters. Unicode (such as UTF-8) is a variable-length encoding that supports over 140,000 characters from all languages.

How do you convert decimal to binary?+

Repeatedly divide the decimal number by 2 and write down the remainders. Reading the remainders in reverse order gives the binary value.

What is the binary representation of letter "A"?+

The letter "A" has an ASCII value of 65. In binary, 65 is represented as 01000001.

How to understand and use this calculator

Numeric Base Mathematics: Positional Representation and Base Conversions

ASCII and Character Encoding: Representing Text in Binary Bytes

Hexadecimal Notation: The Compact Representation of Binary Byte Structures

Bitwise Operations and Hex/Binary Masks in Computer Systems

How to Use This Multi-Base Converter

This is useful for debugging network packets, verifying character encodings, or converting between formats when working with low-level data.

Worked Example: Converting "Hello" Across All Four Formats

Starting from the text "Hello", the calculator encodes each character to its UTF-8 byte value: H=72, e=101, l=108, l=108, o=111.

Related Calculators

Related concepts

Radix (Base)

The number of unique digits, including zero, used to represent numbers in a positional numeral system.

Character Encoding

A set of rules that pairs each character from a repertoire with a unique numerical code.

Bitwise Mask

Data used in bitwise operations to select, set, clear, or toggle specific bits within a byte or word.

Frequently Asked Questions

What is binary?+

Binary is a base-2 numbering system that uses only two digits, 0 and 1, which represent the off and on states of electrical transistors in computer hardware.

What is hexadecimal?+

Hexadecimal is a base-16 numbering system that uses sixteen distinct symbols: 0–9 to represent values zero to nine, and A–F to represent values ten to fifteen.

What does ASCII stand for?+

ASCII stands for American Standard Code for Information Interchange, a character encoding standard for electronic communication.

How do you convert binary to hexadecimal?+

Group the binary bits into sets of four starting from the right. Convert each 4-bit group (nibble) into its equivalent hexadecimal digit (0–F).

Why is hexadecimal used in programming?+

Hexadecimal is used because it represents binary bytes in a compact, human-readable format. One byte (8 bits) can always be written as exactly two hex digits.

What is a nibble?+

A nibble is a four-bit aggregation, or half an octet (half a byte). It represents values from 0 to 15, corresponding to exactly one hexadecimal digit.

How do you represent a space in ASCII?+

A space character is represented by decimal value 32 in the ASCII table, which corresponds to binary 00100000 and hexadecimal 20.

What is the difference between ASCII and Unicode?+

ASCII is a 7-bit encoding representing 128 English characters. Unicode (such as UTF-8) is a variable-length encoding that supports over 140,000 characters from all languages.

How do you convert decimal to binary?+

Repeatedly divide the decimal number by 2 and write down the remainders. Reading the remainders in reverse order gives the binary value.

What is the binary representation of letter "A"?+

The letter "A" has an ASCII value of 65. In binary, 65 is represented as 01000001.

Binary, Hexadecimal, & ASCII Multi-Base Converter

Inputs

Results

Positional Number System Conversions

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Binary, Hexadecimal, & ASCII Multi-Base Converter

Inputs

Results

Key output metrics

Byte Value Distribution

How to understand and use this calculator

Numeric Base Mathematics: Positional Representation and Base Conversions

ASCII and Character Encoding: Representing Text in Binary Bytes

Hexadecimal Notation: The Compact Representation of Binary Byte Structures

Bitwise Operations and Hex/Binary Masks in Computer Systems

How to Use This Multi-Base Converter

Worked Example: Converting "Hello" Across All Four Formats

Related Calculators

Related concepts

Frequently Asked Questions

Positional Number System Conversions

How the calculation works

Learn more about this calculation

How to Use Do The Calculation Calculators: A Practical Step-by-Step Guide

Key output metrics

Byte Value Distribution

How to understand and use this calculator

Numeric Base Mathematics: Positional Representation and Base Conversions

ASCII and Character Encoding: Representing Text in Binary Bytes

Hexadecimal Notation: The Compact Representation of Binary Byte Structures

Bitwise Operations and Hex/Binary Masks in Computer Systems

How to Use This Multi-Base Converter

Worked Example: Converting "Hello" Across All Four Formats

Related Calculators

Related concepts

Frequently Asked Questions