Binary to Decimal Converter
Convert binary numbers to decimal, hexadecimal, and octal. Supports any binary input. Ideal for students and programmers.
Decimal
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Hexadecimal —
Octal —
Extended More scenarios, charts & detailed breakdown ▾
Decimal
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Hexadecimal —
Octal —
Professional Full parameters & maximum detail ▾
Decimal
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Hexadecimal —
Octal —
Bit Count —
Set Bits (1s) —
Least Significant Bit —
Most Significant Bit —
Left Shift <<1 —
Right Shift >>1 —
How to Use This Calculator
- Enter a binary number (only 0s and 1s, e.g. 1010).
- The decimal, hexadecimal, and octal equivalents appear immediately.
- No spaces or prefixes needed — just the binary digits.
Formula
Decimal = sum of (bit × 2^position), reading from right (position 0).
1010 = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10
Example
Example: Convert 11001100 to decimal:
128 + 64 + 0 + 0 + 8 + 4 + 0 + 0 = 204
Frequently Asked Questions
- Binary is a base-2 positional number system that uses only two symbols: 0 and 1. These correspond directly to the two states of electronic circuits (off/on, low voltage/high voltage), making binary the native language of all digital computers, processors, memory chips, and electronic devices. Each binary digit is called a bit (binary digit). Groups of bits represent larger values: 4 bits = a nibble, 8 bits = a byte, 16 bits = a word, 32 bits = a double word (DWORD), 64 bits = a quad word (QWORD). Every piece of data in a computer — text, images, audio, video, programs — is ultimately stored as binary. The binary number system was first described mathematically by Gottfried Wilhelm Leibniz in 1703 and was later found to perfectly mirror Boolean logic (AND, OR, NOT operations).
- To convert binary to decimal, multiply each bit by 2 raised to its positional power (starting from 0 at the rightmost bit), then sum all the results. The bit positions represent: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512... For example, convert 1101: bit positions from right are 0, 1, 2, 3. Calculation: (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13. Another example, 10110: (1×16) + (0×8) + (1×4) + (1×2) + (0×1) = 16 + 0 + 4 + 2 + 0 = 22. A quick check: the value of a binary number is always between 0 and (2^n - 1), where n is the number of bits. An 8-bit number ranges from 0 to 255; a 16-bit number from 0 to 65,535.
- Eight bits form one byte, the fundamental unit of digital storage and memory addressing. A single byte can represent values from 0 (00000000 in binary) to 255 (11111111 in binary) — 256 possible values in total (2⁸ = 256). Bytes are used to measure file sizes, memory, and storage: 1 kilobyte (KB) = 1,024 bytes; 1 megabyte (MB) = 1,048,576 bytes; 1 gigabyte (GB) = 1,073,741,824 bytes. A single ASCII character takes 1 byte; a Unicode character can take 1–4 bytes (UTF-8 encoding). An HD photo might be 3–5 MB (3–5 million bytes); a 4K movie several gigabytes. Note: storage manufacturers often use decimal prefixes (1 GB = 1,000,000,000 bytes) rather than binary prefixes, which is why a "500 GB" hard drive shows as 465 GB in your operating system.
- 11111111 in binary equals 255 in decimal. This is the maximum value representable by 8 bits (1 byte). The calculation: (1×128) + (1×64) + (1×32) + (1×16) + (1×8) + (1×4) + (1×2) + (1×1) = 128+64+32+16+8+4+2+1 = 255. This value is ubiquitous in computing: 255 is the maximum for each RGB color channel (so rgb(255, 255, 255) = white); network subnet masks like 255.255.255.0 use it to indicate "all bits set"; and the hex equivalent is FF (as in #FFFFFF for white). When a signed byte is used, the value 11111111 = −1 in two's complement representation (because the most significant bit indicates a negative number). In unsigned representation, 11111111 = 255.
- Each hexadecimal digit maps exactly to 4 binary bits (a nibble). This perfect correspondence makes binary-to-hex conversion trivial: split the binary number into groups of 4 bits from the right, then convert each group to its hex digit independently. The 16 possible 4-bit combinations map to hex digits 0–9 and A–F: 0000=0, 0001=1, 0010=2, 0011=3, 0100=4, 0101=5, 0110=6, 0111=7, 1000=8, 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F. Example: 11001010 binary → split into 1100 and 1010 → C and A → hex CA. Reverse: CA → 1100 and 1010 → 11001010. Two hex digits always represent exactly one byte (8 bits). This is why color codes, memory addresses, and machine instructions are typically written in hex rather than binary — it is 4× more compact while remaining directly translatable.