What is the binary number system used for?

Binary is the fundamental language of all digital computers. It represents data as sequences of 0s and 1s, corresponding to electrical off/on states. All text, images, programs, and data are ultimately stored in binary.

Binary to Decimal Converter

Q: How do you convert binary to decimal?

Multiply each binary digit by 2 raised to its position power (starting from 0 on the right), then sum all the results. Example: 1101 = 1Ã—8 + 1Ã—4 + 0Ã—2 + 1Ã—1 = 13.

Q: What is 1010 in decimal?

Binary 1010 in decimal is 10. Calculated as: 1Ã—8 + 0Ã—4 + 1Ã—2 + 0Ã—1 = 8 + 2 = 10.

Q: What is 11111111 in decimal?

Binary 11111111 (8 ones) equals decimal 255. This is the maximum value of 1 byte (8 bits).

Convert binary (base 2) numbers to decimal (base 10) instantly with step-by-step calculation shown. Free and works entirely in your browser.

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Binary Number (Base 2 — digits 0 and 1 only)

Binary to Decimal Reference Table

Binary	Decimal	Binary	Decimal
0	0	1000	8
1	1	1001	9
10	2	1010	10
11	3	1100	12
100	4	1111	15
101	5	10000	16
110	6	11111111	255
111	7	10000000	128

How to Convert Binary to Decimal

Converting binary to decimal uses the positional weight method. Each bit (0 or 1) in a binary number has a place value that is a power of 2, starting from 2â° on the right side.

Formula: Decimal = d_nÃ—2ⁿ + … + d₁Ã—2¹ + d₀Ã—2⁰

Example — Convert 1101 to decimal:

Binary:   1  1  0  1
Position: 3  2  1  0
Value:    8  4  0  1

1 Ã— 2Â³ = 1 Ã— 8 = 8
1 Ã— 2Â² = 1 Ã— 4 = 4
0 Ã— 2Â¹ = 0 Ã— 2 = 0
1 Ã— 2â° = 1 Ã— 1 = 1

Total = 8 + 4 + 0 + 1 = 13

Understanding Bit Positions

In a binary number, the rightmost bit is the Least Significant Bit (LSB) with value 2â° = 1. The leftmost bit is the Most Significant Bit (MSB). For an 8-bit number, the positions are: 128, 64, 32, 16, 8, 4, 2, 1 from left to right.

Where Is Binary Used?

Binary numbers appear in many real-world contexts: IP addresses (subnet masks are binary), color codes (RGB values), file permissions in Linux (chmod 755 = 111 101 101 in binary), computer memory addressing, and digital logic circuits.

Frequently Asked Questions

How do you convert binary to decimal?

Multiply each bit by 2 to the power of its position (starting from 0 at the right), then add all the values. Example: 1101 = 1Ã—8 + 1Ã—4 + 0Ã—2 + 1Ã—1 = 13.

What is 1010 in decimal?

Binary 1010 = 1Ã—8 + 0Ã—4 + 1Ã—2 + 0Ã—1 = 10 in decimal.

What is 11111111 in decimal?

Binary 11111111 (eight 1s) = 128+64+32+16+8+4+2+1 = 255. This is the maximum value of one byte.

Why is binary important in computing?

Computers use binary because their electronic components (transistors) have two states: on (1) and off (0). All data — text, images, video, programs — is ultimately stored and processed as binary.