Binary to Decimal Calculator — With Steps
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How to Convert Binary to Decimal
Binary is a base-2 number system using only digits 0 and 1. Each position represents a power of 2, starting from 2^0 on the right. To convert binary to decimal, multiply each digit by its positional value (power of 2) and sum the results.
For example, binary 11010110: 1x128 + 1x64 + 0x32 + 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 128+64+16+4+2 = 214 in decimal. This positional notation works the same way as decimal, just with base 2 instead of base 10.
Binary is the fundamental number system used by computers. All digital data, from text to images to programs, is ultimately stored as binary. Understanding binary conversion is essential for computer science, networking, and digital electronics.
Frequently Asked Questions
Why do computers use binary?
Computers use binary because electronic circuits have two states: on (1) and off (0). This makes binary the most natural and reliable way to represent data electronically. Complex information is built from combinations of these two states.
What is the largest decimal number in 8 bits?
8 bits can represent 2^8 = 256 values, from 0 to 255. The binary number 11111111 = 255 in decimal. This is why many computer values (like RGB color channels) max out at 255.
How do you convert decimal back to binary?
Repeatedly divide by 2 and record the remainders. Read the remainders from bottom to top. For 214: 214/2=107r0, 107/2=53r1, 53/2=26r1, 26/2=13r0, 13/2=6r1, 6/2=3r0, 3/2=1r1, 1/2=0r1 = 11010110.