Number System
Master foundational radix transformations between the core bases of computational science: Base 2 (Binary), Base 8 (Octal), Base 10 (Decimal), and Base 16 (Hexadecimal). Each tool offers step-by-step mathematical proofs with zero-latency execution.
Decimal to Binary
Convert decimal integers (base 10) into pure binary bit patterns with repeated division by 2 steps.
Binary to Decimal
Translate base-2 binary strings into standard base-10 decimal numbers using positional powers of 2.
Decimal to Octal
Convert base-10 decimal numbers into octal notation (base 8) with successive division by 8.
Octal to Decimal
Convert base-8 octal strings into standard decimal values using powers of 8.
Decimal to Hexadecimal
Convert base-10 decimal numbers into hexadecimal notation (0-9, A-F) with repeated division by 16.
Hexadecimal to Decimal
Convert hexadecimal strings (0-9, A-F) into decimal numbers using positional powers of 16.
Binary to Octal
Convert binary sequences into octal by grouping bits into 3-bit triplets from right to left.
Octal to Binary
Convert octal numbers into binary by expanding each octal digit into its 3-bit binary triplet.
Binary to Hexadecimal
Convert binary bit patterns into hexadecimal format by grouping bits into 4-bit nibbles.
Hexadecimal to Binary
Translate hexadecimal characters (0-9, A-F) into pure 4-bit binary nibbles.
Octal to Hexadecimal
Convert octal numbers to hexadecimal format using binary as an intermediate grouping bridge.
Hexadecimal to Octal
Convert hexadecimal strings into octal notation via 4-bit to 3-bit binary regrouping.