Binary Calculator
Convert numbers between binary, decimal, octal, and hexadecimal systems. Perform arithmetic operations in binary.
Binary Operations
Result
1000
= 8 (Decimal)
Conversions
Decimal
42
Binary
101010
Octal
52
Hexadecimal
2A
Bit Representation
02^7
02^6
12^5
02^4
12^3
02^2
12^1
02^0
8 bits = 42
Powers of 2
2^0
1
2^1
2
2^2
4
2^3
8
2^4
16
2^5
32
2^6
64
2^7
128
Binary System
The binary system uses only 0 and 1. Each position represents a power of 2. It's the foundation of all digital computing, as electronic circuits have two states: on (1) and off (0).
Base Conversion
To convert from decimal to binary, repeatedly divide by 2 and read remainders bottom-up. To convert from binary to decimal, sum the powers of 2 where there's a 1.
Logical Operations
AND returns 1 only if both bits are 1. OR returns 1 if at least one bit is 1. XOR returns 1 if bits are different. NOT inverts each bit.