Binary Calculator / Converter
What the Binary Calculator Does
The Binary Calculator / Converter handles base-2 arithmetic and conversions in the numbering system that computers use at the hardware level. It can add, subtract, multiply, and divide binary values on the Calculator tab, then translate results with the Converter options for Binary to Decimal, Decimal to Binary, Binary to Hex, and Hex to Binary.
Students learning number systems, programmers debugging bit-level logic, and electronics hobbyists wiring microcontrollers all reach for this kind of tool. Teachers use it to build clean worked examples, and it saves anyone from head-scratching in bases that decimal-trained brains handle poorly.
How Binary Math Works
Binary uses only 0 and 1, and every position carries a power of 2: 1, 2, 4, 8, 16, 32, 64, and 128 reading right to left. The binary 1011 evaluates as 8 plus 2 plus 1, which is 11 in decimal. Each bit doubles the count of representable values.
Arithmetic still works column by column, but a column overflows once it reaches 2, so 1 plus 1 writes 0 and carries 1. Adding 101 plus 11 gives 1000, which is 8 in decimal. One byte holds 8 bits and expresses any value from 0 to 255.
Using the Calculator Without Mistakes
Choose the Calculator mode for arithmetic or the Converter mode. Select your path such as Binary to Decimal or Hex to Binary, type into the Number field, and press Calculate / Convert.
Always confirm the input base first, because 10 means ten in decimal but two in binary. Avoid spaces in the input, drop leading zeros for tidiness, and double check results by converting the answer back the opposite way.
Frequently Asked Questions
What is binary 1011 in decimal?
Binary 1011 converts to 11 in decimal. Each bit carries a power of 2, so 1011 equals 8 plus 2 plus 1, which gives 11.
How many values can one byte hold?
One byte contains 8 bits, so it stores 2 to the 8th power, or 256 values. That range runs from 0 through 255 in decimal.
What powers of 2 should I memorize?
The first eight place values are 1, 2, 4, 8, 16, 32, 64, and 128. Knowing these lets you read an 8-bit binary number at a glance.
Why do programmers use hex with binary?
One hex digit maps exactly to 4 bits, so a byte becomes two hex digits instead of eight binary ones. The pattern 11111111 reads as FF, which is far easier to scan.
How does binary addition carry work?
Binary addition carries whenever a column totals 2, writing 0 in that column and carrying 1 leftward. So 1101 plus 0011 produces 10000, which is 16 in decimal.