Binary is base 2 — a number system using only two digits: 0 and 1. Every digital computer stores all data as binary because transistors have two stable states: on (1) and off (0). The word 'binary' comes from the Latin bini meaning 'two together'.

How do you convert binary to decimal?

Multiply each bit by its place value (power of 2) and add the results. Example: 1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 8 + 0 + 2 + 0 = 10₁₀ The rightmost bit is always 2^0 = 1. Moving left each position doubles: 1, 2, 4, 8, 16, 32, 64, 128...

How do you convert binary to hex?

Group binary digits into groups of 4 from the right. Each group of 4 bits maps directly to one hex digit: 0000=0, 0001=1, ..., 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F Example: 11111111₂ → 1111 1111 → FF₁₆ Example: 1010₂ → 0000 1010 → 0A₁₆ = A₁₆

Why does binary always end in 0 for even and 1 for odd?

The rightmost bit represents 2^0 = 1. Every other bit position (2^1=2, 2^2=4...) is even. So the total is even if and only if the last bit is 0. This is why you can instantly tell if a binary number is even or odd just by looking at the last digit.

What is the largest number that fits in N bits?

N bits can represent 2^N values (0 to 2^N - 1). 4 bits: 0–15 (1111₂ = F₁₆) 8 bits: 0–255 (11111111₂ = FF₁₆) 16 bits: 0–65,535 32 bits: 0–4,294,967,295 64 bits: 0–18,446,744,073,709,551,615 All-1s pattern in N bits = 2^N - 1.

Binary Mega — Convert Any Binary Number Instantly

The Binary Mega Calculator converts any binary number (base 2) to decimal, hexadecimal, and octal instantly. Enter any sequence of 0s and 1s — the result appears immediately with a full bit visualiser showing every active bit, a place value breakdown, step-by-step conversion, and a CSS colour swatch...

ENTER BINARY NUMBER

BINARY (digits 0 and 1 only)

0b

QUICK EXAMPLES

CONVERSIONS

DECIMAL (base 10)

HEX (base 16)

0xA

OCTAL (base 8)

PLACE VALUE BREAKDOWN

8 (2^3) + 2 (2^1) = 10

CSS GREYSCALE COLOUR #0A0A0A

#0A0A0A

rgb(10, 10, 10)

BIT VISUALISER (8-BIT)

0

2^7

0

2^6

0

2^5

0

2^4

1

2^3

0

2^2

1

2^1

0

2^0

2 active bits of 8

BASE CONVERSION SUMMARY

Binary (2)1010₂

Decimal (10)10₁₀

Octal (8)12₈

Hex (16)0xA

BINARY QUICK REFERENCE

Last bit is 0→ even number

Last bit is 1→ odd number

Single 1 + zeros→ power of 2

All 1s (n bits)→ 2ⁿ - 1

1 hex digit= 4 binary bits (nibble)

2 hex digits= 8 binary bits (byte)

11111111₂= 255 = 0xFF

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type any binary number using only 0s and 1s into the input box. The 0b prefix is shown automatically — do not type it. Invalid characters (any digit other than 0 or 1) are silently ignored.
2
The result panel shows the decimal value in green, hex in gold, and octal in blue. All three update instantly as you type — no submit button needed.
3
The bit visualiser on the right shows every bit as a coloured square: black with green text for 1-bits, grey for 0-bits. The place value of each bit position (2^n) is shown beneath it.
4
For values up to 255, a greyscale CSS colour chip shows what rgb(n,n,n) looks like — making binary immediately visual. Click COPY to copy the full result string. Click SHARE to get a URL with your binary number embedded (?n=1010).

WORKED EXAMPLE

Convert 11111111₂ to decimal, hex, and octal: 1×2^7 + 1×2^6 + 1×2^5 + 1×2^4 + 1×2^3 + 1×2^2 + 1×2^1 + 1×2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255₁₀ = 0xFF = 377₈ All 8 bits active means 2^8 - 1 = 255 — the maximum value of one byte.

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

Decimal 8 to Hex

Calculate instantly →

Decimal 8 to Binary

Calculate instantly →

Decimal 2 to Hex

Calculate instantly →

100 in Binary

Calculate instantly →

Was this calculator helpful?

Last updated: April 29, 2026 · Verified by EagleCalculator team · Eagle-eyed accuracy for every calculation.

Binary Mega — Convert Any Binary Number Instantly

ENTER BINARY NUMBER

HOW TO USE

WORKED EXAMPLE

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

MORE NUMBER THEORY CALCULATORS