Complete Tools Library
Deterministic, hardware-grade calculations for binary arithmetic, radix transformations, signed registers, and digital logic. All 100% private and computed in-browser.
Number System
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.
Binary Tools
Binary Addition Calculator
Add two binary numbers with step-by-step column-by-column carry bits and sum bits.
Binary Subtraction Calculator
Subtract one binary number from another with column borrow tracking and Two’s Complement verification.
Binary Multiplication Calculator
Multiply binary numbers with partial products, shift-and-add rows, and step-by-step proofs.
Binary Division Calculator
Divide binary numbers with step-by-step long division, quotient, and remainder tracking.
Binary to Gray Code Converter
Convert natural binary numbers to reflected Gray code using bitwise shift and XOR logic.
Gray Code to Binary Converter
Convert reflected Gray code back to standard natural binary using sequential XOR cascade.
Binary to BCD Converter
Convert binary integers into 8421 Binary-Coded Decimal (BCD) 4-bit nibbles.
BCD to Binary Converter
Convert 8421 Binary-Coded Decimal (BCD) nibbles back to standard positional binary.
Binary to Excess-3 Converter
Convert binary numbers into Excess-3 (XS-3 / Stibitz) self-complementing code.
Excess-3 to Binary Converter
Convert Excess-3 (XS-3) code nibbles back into standard natural binary.
Binary Bit Calculator
Analyze binary strings: count set bits (Hamming weight), total length, leading/trailing zeros, and parity.
Binary Fraction Converter
Convert fractional binary numbers into decimal fractions and vice versa with negative powers of 2.
Binary Floating-Point Converter
Dissect real decimal numbers into binary floating-point scientific notation (significand and exponent).
Binary Number Validator
Verify if a string is a valid binary sequence and inspect character legality, length, and format.
Decimal Tools
convert decimal fraction to binary
Convert continuous decimal fractions (e.g. 0.625) into binary fractions using repeated multiplication by 2.
Decimal to BCD Converter
Convert standard base-10 decimal numbers into 8421 Binary-Coded Decimal (BCD) 4-bit nibbles.
Octal Tools
Octal to Binary
Convert octal numbers into binary by expanding each octal digit into its 3-bit binary triplet.
Binary to Octal
Convert binary sequences into octal by grouping bits into 3-bit triplets from right to left.
Octal to Decimal
Convert base-8 octal strings into standard decimal values using powers of 8.
Decimal to Octal
Convert base-10 decimal numbers into octal notation (base 8) with successive division by 8.
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.
Octal Arithmetic Calculator
Perform addition, subtraction, multiplication, and division directly on base-8 octal numbers.
Octal Number Validator
Verify if a number string is a valid base-8 octal representation and check for illegal digits (8 and 9).
Hexadecimal Tools
Hex to Binary
Convert hex characters into 4-bit binary nibbles instantly with zero latency.
Binary to Hex
Convert binary strings into hexadecimal notation by grouping into 4-bit nibbles.
Hex to Decimal
Convert hexadecimal strings into base-10 decimal numbers using positional powers of 16.
Decimal to Hex
Convert decimal integers into hexadecimal strings with successive division by 16.
Hex to Octal
Convert hexadecimal strings into octal format via 4-bit to 3-bit binary regrouping.
Octal to Hex
Convert octal numbers into hexadecimal format using 3-bit to 4-bit binary regrouping.
Hexadecimal Addition
Add hexadecimal numbers with column carries, base-16 wrapping, and step-by-step proofs.
Hexadecimal Subtraction
Subtract hexadecimal numbers with column borrows of 16 and step-by-step proofs.
Hexadecimal Multiplication
Multiply hexadecimal numbers with base-16 partial products and step-by-step proofs.
Hexadecimal Division
Divide hexadecimal numbers with step-by-step base-16 long division, quotient, and remainder.
Hexadecimal Number Validator
Verify if a string is a valid base-16 hexadecimal representation and check allowable characters.
Complement Tools
1's Complement Calculator
Calculate the 1’s complement of binary numbers by inverting every bit (bitwise NOT).
2's Complement Calculator
Compute the 2’s complement for signed binary numbers across 8, 16, 32, and 64-bit architectures.
9's Complement Calculator
Calculate the 9’s complement of decimal numbers by subtracting each digit from 9.
10's Complement Calculator
Calculate the 10’s complement of decimal numbers by taking the 9’s complement and adding 1.
1's ↔ 2's Complement Converter
Convert seamlessly between 1’s complement and 2’s complement representations with step-by-step proofs.
Signed Binary Calculator
Analyze signed binary numbers across Signed Magnitude, 1’s Complement, and 2’s Complement formats.
Sign-Magnitude Converter
Convert signed decimal numbers to Sign-Magnitude binary format and decode sign-magnitude bits.
1's Complement Representation
Inspect how positive and negative numbers map to bit patterns under 1’s Complement notation.
2's Complement Representation
Visualize 2’s complement bit mappings, negative weighting of the MSB, and asymmetric range limits.
Signed Integer Range Calculator
Calculate exact minimum and maximum limits for signed integers across custom and standard bit widths.
Digital Electronics Tools
Bit Calculator
Calculate storage sizes, bandwidth rates, bit combinations, and binary data units.
Bit to Byte Converter
Convert data quantities between bits (b) and bytes (B) with exact fractions and decimal equivalents.
Byte to KB/MB/GB/TB Converter
Convert storage sizes across Bytes, Kilobytes, Megabytes, Gigabytes, and Terabytes (both 1000 and 1024 standards).
Binary Bit Shift Calculator
Simulate logical and arithmetic bit shifts (left, right, zero-fill) on binary registers.
Left Shift Calculator
Compute bitwise left shifts (<<) to multiply binary numbers by powers of 2.
Right Shift Calculator
Compute bitwise right shifts (>>) to divide binary numbers by powers of 2.
Arithmetic Shift Calculator
Compute arithmetic right shifts with sign-bit preservation (replicated MSB) for signed integers.
Logical Shift Calculator
Compute logical bit shifts (left and zero-fill right) for unsigned integers and raw bit patterns.
Rotate Left Calculator
Compute circular bit rotation left (ROL) where bits falling off the MSB wrap around to the LSB.
Rotate Right Calculator
Compute circular bit rotation right (ROR) where bits falling off the LSB wrap around to the MSB.
Bitwise AND Calculator
Compute bitwise AND (&) between two binary numbers to mask, clear, and isolate specific bits.
Bitwise OR Calculator
Compute bitwise OR (|) between two binary numbers to set and combine bit flags.
Bitwise XOR Calculator
Compute bitwise XOR (^) to toggle bits, compute parity, and implement basic encryption.
Bitwise NOT Calculator
Compute bitwise NOT (~) to invert all bits in an operand across 8, 16, 32, and 64-bit registers.
NAND Calculator
Compute the universal NAND logic operation (NOT AND) with full truth tables and proofs.
NOR Calculator
Compute the universal NOR logic operation (NOT OR) with full truth tables and circuit proofs.
XNOR Calculator
Compute the XNOR logic operation (Exclusive NOR / Equivalence gate) with complete truth tables.
Coding & Computer Number Tools
ASCII to Binary Converter
Convert plain text and ASCII characters into 8-bit binary byte sequences.
Binary to ASCII Converter
Decode 8-bit binary byte sequences back into readable ASCII text characters.
ASCII to Hex Converter
Convert text characters into hexadecimal byte sequences (0x00 to 0xFF).
Hex to ASCII Converter
Convert hexadecimal byte strings back into readable ASCII text characters.
Unicode to Hex Converter
Convert Unicode characters, emojis, and symbols to hex codepoints (U+XXXX) and UTF-8 hex bytes.
Unicode to Binary Converter
Convert Unicode characters into raw UTF-8 binary bit patterns with leading continuation markers.
RGB to Hex Converter
Convert Red, Green, and Blue decimal color channels (0-255) into web-standard 6-character hex color codes.
Hex to RGB Converter
Convert 6-digit and 3-digit hex color strings into decimal RGB channels (0-255) with live color preview.
IPv4 to Binary Converter
Convert dotted-decimal IPv4 addresses (e.g. 192.168.1.1) into 32-bit binary bitstreams.
Binary to IPv4 Converter
Convert 32-bit binary bitstreams back into standard dotted-decimal IPv4 addresses.
MAC Address to Binary
Convert 48-bit Ethernet hardware MAC addresses into binary bitstreams.
MAC Address to Hex
Normalize and format MAC address representations across colon, hyphen, Cisco dot, and raw hex formats.
Unix Timestamp to Binary/Hex
Convert Unix epoch timestamps into 32-bit and 64-bit binary and hexadecimal representations with UTC date.
Hex Color Converter
Convert hex colors to RGB, HSL, CMYK, and 24-bit integer values with live color palette swatch.
Character to ASCII to Binary
Step-by-step conversion of single characters to decimal ASCII codes and 8-bit binary bytes.
Character to ASCII to Hex
Step-by-step conversion of single characters to decimal ASCII codes and 2-digit hexadecimal bytes.
Base Conversion Tools
Base 2 Converter
Convert numbers into and out of binary (base 2) across all common and custom radices.
Base-3 Converter
Convert numbers into and out of ternary (base 3) using digits 0, 1, and 2 with powers of 3.
Base-4 Converter
Convert numbers into and out of quaternary (base 4) notation using digits 0, 1, 2, and 3.
Base-5 Converter
Convert numbers into and out of quinary (base 5) using digits 0, 1, 2, 3, and 4.
Base-6 Converter
Convert numbers into and out of senary (base 6) using digits 0 through 5.
Base-7 Converter
Convert numbers into and out of septenary (base 7) using digits 0 through 6.
Base-8 Converter
Convert numbers into and out of octal (base 8) notation across all computing radices.
Base-9 Converter
Convert numbers into and out of nonary (base 9) using digits 0 through 8.
Base-10 Converter
Convert standard decimal numbers into any other radix from base 2 to base 36.
Base-11 Converter
Convert numbers into and out of undecimal (base 11) using digits 0-9 and letter A.
Base-12 Converter
Convert numbers into and out of duodecimal (base 12) using digits 0-9, A, and B.
Base-13 Converter
Convert numbers into and out of tridecimal (base 13) using digits 0-9 and letters A, B, C.
Base-14 Converter
Convert numbers into and out of tetradecimal (base 14) using digits 0-9 and A, B, C, D.
Base-15 Converter
Convert numbers into and out of pentadecimal (base 15) using digits 0-9 and A through E.
Base-16 Converter
Convert numbers into and out of hexadecimal (base 16) across any custom radix.
Any Base → Any Base Converter
Convert any number between any source base (2 to 36) and any target base (2 to 36).
Base-N Number Validator
Verify if a number string is mathematically valid for any chosen radix (base 2 through 36).
Custom Base Converter
Configure arbitrary custom radices with user-defined alphabets and symbol sets.
Number System Arithmetic
Binary Calculator
All-in-one binary arithmetic calculator for addition, subtraction, multiplication, and division.
Octal Calculator
All-in-one octal calculator for addition, subtraction, multiplication, and division in base 8.
Hexadecimal Calculator
Complete hexadecimal calculator for addition, subtraction, multiplication, and division in base 16.
Base-N Addition
Add two numbers in any arbitrary radix from base 2 to base 36 with column carry tracking.
Base-N Subtraction
Subtract numbers in any arbitrary radix from base 2 to base 36 with column borrow tracking.
Base-N Multiplication
Multiply numbers in any arbitrary radix (base 2 to 36) with base-N partial products.
Base-N Division
Divide numbers in any radix (base 2 to 36) with step-by-step long division, quotient, and remainder.
Base-N Modulo Calculator
Compute modulo remainders (A mod B) directly in any base from base 2 to base 36.
Base-N Power Calculator
Calculate exponentiation (A^B) directly in any base from base 2 to base 36.
Number Representation Tools
Signed Number Calculator
Evaluate signed integers across 8, 16, 32, and 64-bit Two’s Complement representations.
Unsigned Number Calculator
Calculate unsigned integer capacity, binary bit patterns, and maximum values from 0 to 2^n - 1.
Integer Range Calculator
Calculate signed and unsigned limits for any register width from 1 to 128 bits.
4-bit Number Range Calculator
Analyze the 4-bit nibble register range: signed -8 to +7 and unsigned 0 to 15.
8-bit Number Range Calculator
Analyze 8-bit byte register limits: signed -128 to +127 and unsigned 0 to 255.
16-bit Number Range Calculator
Analyze 16-bit word limits: signed -32,768 to +32,767 and unsigned 0 to 65,535.
32-bit Number Range Calculator
Analyze 32-bit dword limits: signed ±2.14 billion and unsigned 0 to 4.29 billion.
64-bit Number Range Calculator
Analyze 64-bit qword limits: signed ±9.22 quintillion and unsigned 0 to 18.44 quintillion.
Two's Complement Range Calculator
Calculate the asymmetric signed range [-2^(n-1) to +2^(n-1)-1] for any bit width n.
Floating Point Representation Calculator
Analyze real numbers in computer memory: sign bit, biased exponent, and significand fraction.
IEEE 754 Converter
Convert decimal real numbers into IEEE-754 32-bit Single Precision and 64-bit Double Precision formats.
IEEE 754 to Decimal
Convert 32-bit and 64-bit IEEE 754 binary or hex bit patterns back into real decimal numbers.
Decimal to IEEE 754
Convert real decimal numbers directly into IEEE 754 Single Precision and Double Precision bit patterns.
Float32 Converter
Specialized 32-bit Single Precision IEEE 754 float converter with exact rounding error analysis.
Float64 Converter
Specialized 64-bit Double Precision IEEE 754 float converter with 53-bit significand analysis.
Educational Number System Tools
Number System Quiz
Test your understanding of binary, octal, decimal, and hexadecimal with interactive questions.
Binary Conversion Quiz
Practice and test binary to decimal, hex, and octal conversions with instant score tracking.
Hexadecimal Quiz
Master hexadecimal conversions, letters A through F, and 4-bit nibble mappings.
Octal Quiz
Test your base-8 knowledge: 3-bit triplets, octal arithmetic, and Unix permission modes.
Complement Quiz
Test your understanding of 1’s, 2’s, 9’s, and 10’s complements and signed register ranges.
Base Conversion Practice
Interactive practice generator: solve dynamically generated base conversion problems with hints and proofs.
Binary Arithmetic Practice
Practice binary addition, subtraction, multiplication, and division with instant solution checking.
Random Number System Generator
Generate random numbers in binary, octal, decimal, or hexadecimal across custom bit widths.
Step-by-Step Conversion Solver
Universal multi-radix solver showing every mathematical step, division table, and expansion row.
Number System Formula Sheet
Comprehensive reference of all mathematical formulas, complement equations, and radix conversion algorithms.
Number System Cheat Sheet
Quick-reference lookup tables: powers of 2, hex/octal/binary mapping, ASCII codes, and logic gates.
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