No saved tools yet. Perform binary arithmetic (add, subtract, multiply, divide) and bitwise operations (AND, OR, XOR, NOT, shifts). Interactive step-by-step solutions with multi-base results in binary, decimal, and hexadecimal. ✓ Free to use ✓ No sign-up required ↻ Updated Jan 2026 Binary Calculator Try it now — free ▼ Binary Calculator Binary Converter Hex Calculator Hex Converter Decimal to Binary Hex to Binary Embed Binary Calculator Widget ✓ Free to use ✓ No sign-up required ↻ Updated Jan 2026 Binary Calculator Try it now — free ▼ Binary Calculator Binary Converter Hex Calculator Hex Converter Decimal to Binary Hex to Binary Embed Binary Calculator Widget Embed Binary Calculator Widget Your ad blocker is preventing us from showing ads MiniWebtool is free because of ads. If this tool helped you, please support us by upgrading for ad-free browsing and more daily uses, or allowlist MiniWebtool.com and reload. Allow ads for MiniWebtool.com, then reload Or upgrade for ad-free browsing and higher daily limits About Binary Calculator Welcome to the Binary Calculator , a comprehensive free online tool for performing binary arithmetic and bitwise operations. Whether you are a student learning computer science, a programmer debugging low-level code, or an electronics enthusiast working with digital systems, this calculator provides detailed step-by-step solutions with results displayed in multiple number bases. What is Binary? Binary is a base-2 numeral system that uses only two digits: 0 and 1. Each digit in a binary number is called a bit (binary digit). Binary is the foundation of all modern computing because electronic circuits can easily represent two states: on (1) and off (0). Understanding Binary Place Values Each position in a binary number represents a power of 2, starting from 2 0 (which equals 1) on the right: Binary Arithmetic Operations Binary Addition Binary addition follows these simple rules: 1 + 1 = 10 (write 0, carry 1 to the next column) 1 + 1 + 1 = 11 (write 1, carry 1) Binary Subtraction Binary subtraction uses borrowing when needed: 0 - 1 : Borrow 1 from the next column, making it 10 - 1 = 1 Binary Multiplication Binary multiplication is simpler than decimal because you only multiply by 0 or 1: Binary Division Binary division works like long division in decimal but uses binary subtraction. This calculator handles both integer division and fractional results. Bitwise Operations AND Operation (&) Returns 1 only when both corresponding bits are 1. Used for masking specific bits. OR Operation (|) Returns 1 when either corresponding bit is 1. Used for setting specific bits. XOR Operation (^) Returns 1 when corresponding bits are different . Used for toggling bits and simple encryption. NOT Operation (~) Flips all bits: 0 becomes 1, and 1 becomes 0. Left Shift (<<) and Right Shift (>>) Shifts move all bits left or right by the specified number of positions: Left shift multiplies by 2 for each position shifted Right shift divides by 2 for each position shifted How to Use This Calculator Enter first binary number: Type your first binary number using only 0s and 1s. You can use the quick example buttons to try common calculations. Select operation: Choose your operation: arithmetic (+, -, *, /, %) or bitwise (AND, OR, XOR, NOT, <<, >>). Click operation buttons or use the dropdown. Enter second binary number: Input your second binary number. For NOT operation, only the first number is needed. For shifts, this is the number of positions to shift. View results: Click Calculate to see results in binary, decimal, and hexadecimal formats with step-by-step solution breakdown and interactive diagrams. Frequently Asked Questions What is binary and how does it work? Binary is a base-2 numeral system that uses only two digits: 0 and 1. Each digit represents a power of 2, from right to left. For example, 1010 in binary equals 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal. Computers use binary because electronic circuits can easily represent two states: on (1) and off (0). How do you add binary numbers?

Binary addition follows simple rules: 0+0=0, 0+1=1, 1+0=1, and 1+1=10 (write 0, carry 1). Add column by column from right to left, carrying when the sum is 2 or more. For example, 1011 + 1101: starting from right, 1+1=10 (write 0, carry 1), 1+0+1=10 (write 0, carry 1), 0+1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1). Result: 11000. What are bitwise operations in binary? Bitwise operations manipulate individual bits in binary numbers. AND (&) returns 1 only if both bits are 1. OR (|) returns 1 if either bit is 1. XOR (^) returns 1 if bits are different. NOT (~) flips all bits. Left shift (<<) moves bits left, multiplying by 2. Right shift (>>) moves bits right, dividing by 2. These are essential for low-level programming and optimization. How do you multiply binary numbers? Binary multiplication works like decimal multiplication but simpler: 0×0=0, 0×1=0, 1×0=0, 1×1=1. Multiply the multiplicand by each bit of the multiplier, shift left for each position, then add all partial products. For example, 101 × 11: 101×1=101, 101×1 shifted left = 1010, then add: 101 + 1010 = 1111 (15 in decimal, which is 5×3). What is the difference between signed and unsigned binary? Unsigned binary represents only positive numbers (0 and above). Signed binary uses the leftmost bit as a sign bit: 0 for positive, 1 for negative. The most common signed representation is two's complement, where negative numbers are represented by inverting all bits and adding 1. This calculator supports both positive and negative binary numbers for arithmetic operations. Related Resources Binary Number - Wikipedia Bits and Binary - Khan Academy Binary Converter - Convert between binary, decimal, hex, and octal Hex Calculator - Perform hexadecimal arithmetic and bitwise operations Hex Converter - Convert hexadecimal numbers Reference this content, page, or tool as: "Binary Calculator" at https://MiniWebtool.com/binary-calculator/ from MiniWebtool , https://MiniWebtool.com/ by miniwebtool team. Updated: Jan 10, 2026 Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs "Binary Calculator" at https://MiniWebtool.com/binary-calculator/ from MiniWebtool , https://MiniWebtool.com/ by miniwebtool team. Updated: Jan 10, 2026 Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs by miniwebtool team. Updated: Jan 10, 2026 You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer. Number System Converters: Base-N Calculator Binary Calculator Binary Converter Binary to Decimal Converter Binary to Hex Converter Binary to Octal Converter Decimal to Binary Converter Decimal to Hex Converter Decimal to Octal Converter Decimal to Percent Converter Decimal to Scientific Notation Converter Degree to Radian Converter Hex to Binary Converter Hex to Decimal Converter Hex to Octal Converter Octal Calculator Popular Octal Converter Octal to Binary Converter Octal to Decimal Converter Octal to Hex Converter Percent to Decimal Converter Radian to Degree Converter Ratio to Percentage Calculator Popular Roman Numerals Converter Popular Scientific Notation to Decimal Converter Popular Binary Calculator ©MiniWebtool.com EMBED THE WIDGET Copy The Source Code Tip: The widget is responsive to mobile devices. If the set width is larger than the device screen width, it will be automatically adjusted to 100% of the screen width. On the preview mode the width is limited to 500. You can change data-width to any value based on your website layout. By embedding MiniWebtool widgets on your site, you are agreeing to our Terms of Service. By embedding MiniWebtool widgets on your site, you are agreeing to our Terms of Service.