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Matematika

Binary Decimal Calculator

Number Base Converter

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What is Binary Decimal Calculator?

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A binary to decimal (and decimal to binary) converter translates between base 2 and base 10. Binary is the native language of digital computers; decimal is the human number system.

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Vzorec

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f(x)Binary to decimal: Σ (bit value × 2^position); Decimal to binary: repeatedly divide by 2, read remainders in reverse

Variable Legend

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SymbolJménoJednotkaPopis
bBinary digit (0 or 1)——
dDecimal value——
nBit position (rightmost = 0)——

How to Binary Decimal Calculator

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  1. 1Binary to decimal: each bit position = 2ⁿ, sum the 1-positions
  2. 2Decimal to binary: divide by 2 repeatedly, read remainders in reverse
  3. 38-bit byte: values 0–255; 16-bit: 0–65,535
  4. 4Signed integers use two's complement for negative numbers

Worked Examples

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Example 1
Given:Binary 11001010
Výsledek:128+64+0+0+8+0+2+0 = 202 decimal

Real-World Applications

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Understanding computer memory

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Low-level programming and assembly

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Networking and IP addressing

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Digital signal processing

Powers of 2

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Bit position2ⁿ value
01
12
24
38
416
7128
8256
1532,768

Frequently Asked Questions

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Q

Why do computers use binary?

A

Binary matches the on/off states of transistors in circuits. 1 = on/high voltage, 0 = off/low voltage.

Q

What is a byte?

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A byte is 8 bits. It can represent values from 0 (00000000) to 255 (11111111).

Q

How are negative numbers represented?

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Two's complement: flip all bits and add 1. Example: −5 as 8-bit = 11111011.

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Reviewed October 2026
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