Binary Calculator - Operations
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Formula: Binary: base-2 number system (0 and 1)
Worked example — 10110 (22)
Binary: base-2 number system (0 and 1)
Perform arithmetic and bitwise operations on binary numbers. Convert between binary and decimal.
Problem:1010 + 1100
Solution:10 + 12 = 22 = 10110
Result:10110 (22)
Same as decimal but carry at 2 instead of 10. 0+0=0, 0+1=1, 1+1=10 (carry 1), 1+1+1=11 (carry 1).
AND outputs 1 only when both bits are 1. OR outputs 1 when at least one bit is 1. XOR outputs 1 only when bits differ. These are the building blocks of all digital logic in processors.
Multiply each bit by its positional power of 2 and sum the results. For 1101: (1×8)+(1×4)+(0×2)+(1×1) = 8+4+0+1 = 13. Binary Calculator - Operations shows the decimal equivalent automatically.
Binary operations are essential for embedded systems programming, network mask calculations (subnetting), bit flags in game engines, cryptography, and understanding how CPUs perform arithmetic at the hardware level.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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