Convert Binary to Decimal: Easy Step-by-Step
Your homework says convert 10110101 to decimal. You are staring at ones and zeros. Let me show you exactly how to do it.
Quick Answer
Multiply each binary digit by its power of 2 and add them up. Or paste any binary number into the free converter at dotsapps.com for instant results.
How Binary Numbers Work
Binary uses only two digits: 0 and 1. Each position is worth twice as much as the one to its right. This is just like decimal, where each position is worth ten times more.
In decimal, 345 means 3×100 + 4×10 + 5×1. In binary, 101 means 1×4 + 0×2 + 1×1 = 5.
Computers use binary because electronic switches are either on (1) or off (0). Every number, letter, and image on your screen is stored as binary deep down.
Step-by-Step Binary to Decimal Conversion
Let's convert 10110101 to decimal.
- Write out the powers of 2 from right to left: 1, 2, 4, 8, 16, 32, 64, 128
- Line up each binary digit with its power of 2
- Multiply each digit by its power
- Add all the results
Here is the math:
- 1×128 = 128
- 0×64 = 0
- 1×32 = 32
- 1×16 = 16
- 0×8 = 0
- 1×4 = 4
- 0×2 = 0
- 1×1 = 1
128 + 0 + 32 + 16 + 0 + 4 + 0 + 1 = 181
Common Binary to Decimal Values
Memorize these and conversions get faster:
- 0001 = 1
- 0010 = 2
- 0100 = 4
- 1000 = 8
- 1111 = 15
- 11111111 = 255 (one byte)
The number 255 shows up everywhere in computing. It is the maximum value of a single byte. That is why RGB colors go from 0 to 255.
Why Students Need Binary Conversion Skills
Computer science courses expect you to convert between number bases by hand. It shows up on exams and in coding interviews.
Understanding binary also helps you grasp how computers store data, how IP addresses work, and how file sizes are calculated.
For quick answers and checking your work, use the free converter tool. But learn the method too — it will help you in the long run.
How to Do It: Step-by-Step
- 1
Go to the Number Base Converter at dotsapps.com
- 2
Select Binary (base 2) as the input format
- 3
Type or paste your binary number (like 10110101)
- 4
Read the decimal result instantly — plus octal and hex too
- 5
Click Copy to grab the answer
Frequently Asked Questions
What is 11111111 in decimal?
11111111 in binary equals 255 in decimal. This is the largest number you can store in 8 bits (one byte).
How do you convert decimal to binary?
Divide the decimal number by 2 over and over. Write down each remainder. Read the remainders from bottom to top. That is your binary number.
Why do computers use binary?
Computer chips use tiny switches that are either on or off. Binary (1 and 0) maps perfectly to these two states. It is the simplest way to store and process data electronically.
What is the binary for 100?
100 in decimal is 1100100 in binary. You can verify this: 64 + 32 + 4 = 100.
Is there a quick trick for binary to decimal?
Yes. Memorize the powers of 2 (1, 2, 4, 8, 16, 32, 64, 128, 256). Then just add the powers where the binary digit is 1. Skip the zeros.
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