🔢 All Bases — Live Converter

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Decimal Base 10

Binary Base 2

Hexadecimal Base 16

Octal Base 8

Quick Values

⚙️ Bitwise Operations

Enter two decimal numbers and select an operation.

Operand A (Decimal)

Operand B (Decimal)

A (Binary)—

B (Binary)—

AND Result—

Result (Binary)—

Result (Hex)—

Operation Reference

🔵

AND

1 only if both bits are 1.
Uses: masking, clearing bits

🟢

1 if either bit is 1.
Uses: setting bits

🟡

XOR

1 if bits are different.
Uses: toggling, encryption

🔴

NOT

Flips all bits (0→1, 1→0).
Uses: complementing

⬅️

Left Shift (<<)

Shifts bits left, multiplies by 2.
Uses: fast multiplication

➡️

Right Shift (>>)

Shifts bits right, divides by 2.
Uses: fast division

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📋 Decimal / Binary / Hex / Octal Reference

Common values across all 4 number systems.

Decimal	Binary	Hex	Octal	Notes

📐 How Number Systems Work

Positional Number Systems

Every number system uses positional notation — each digit's value depends on its position (place value).

Decimal (Base 10): digits 0–9
Binary (Base 2): digits 0–1
Octal (Base 8): digits 0–7
Hex (Base 16): digits 0–9, A–F

Value = Σ (digit × base^position)

Example: Decimal 255
= 2×10² + 5×10¹ + 5×10⁰
= 200 + 50 + 5 = 255

Decimal → Binary

Repeatedly divide by 2 and record remainders (read bottom to top).

Convert 13 to Binary:
13 ÷ 2 = 6 remainder 1 ↑
6 ÷ 2 = 3 remainder 0 ↑
3 ÷ 2 = 1 remainder 1 ↑
1 ÷ 2 = 0 remainder 1 ↑
Result: 1101 (read upward)

Binary → Decimal

Multiply each bit by its power of 2 and sum them.

Convert 1101 to Decimal:
1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 8 + 4 + 0 + 1
= 13

Decimal → Hexadecimal

Divide by 16, record remainders using 0–9 and A–F.

Convert 255 to Hex:
255 ÷ 16 = 15 remainder 15 → F ↑
15 ÷ 16 = 0 remainder 15 → F ↑
Result: FF

Hex → Binary (Shortcut)

Each hex digit = exactly 4 binary bits. Convert each digit independently.

Convert 1A3F to Binary:
1 → 0001
A → 1010
3 → 0011
F → 1111
Result: 0001 1010 0011 1111

Why Programmers Love Hex

1 byte = 8 bits = exactly 2 hex digits
FF hex = 1111 1111 binary = 255 decimal

Colors in web: #FF5733
= R:FF(255) G:57(87) B:33(51)

Memory addresses: 0x7FFF0000
IPv6 addresses: 2001:0db8:85a3::8a2e

❓ Frequently Asked Questions

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