Binary to Decimal Converter — How to Convert Binary Numbers (With Chart & Calculator)

To convert binary to decimal, multiply each bit by its power of 2 and add them up. For example, 1101 in binary = (1 times 8) + (1 times 4) + (0 times 2) + (1 times 1) = 13 in decimal. Or just paste your binary number into our converter for instant results.

Whether you are learning computer science, debugging network configurations, or just curious about how computers think, understanding binary-to-decimal conversion is a foundational skill. This guide gives you the method, a reference chart you can bookmark, and a free calculator that handles the math instantly.

Binary to Decimal Reference Chart

Here are the most commonly referenced binary-to-decimal-to-hex conversions. Bookmark this table — you will use it more than you think.

Binary	Decimal	Hex
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	8
1001	9	9
1010	10	A
1011	11	B
1100	12	C
1101	13	D
1110	14	E
1111	15	F
100000	32	20
1000000	64	40
10000000	128	80
11111111	255	FF
100000000	256	100
1000000000	512	200
10000000000	1024	400
1111111111111111	65535	FFFF

Powers of 2 Table

Every binary digit represents a power of 2. Memorize the first 10 and you can convert most values in your head.

Power	Value	Common Use
2^0	1	Least significant bit
2^1	2	—
2^2	4	—
2^3	8	Octal digit range (0-7)
2^4	16	Hex digit range (0-F)
2^5	32	—
2^6	64	—
2^7	128	Signed byte range (-128 to 127)
2^8	256	One byte (0-255), RGB color values
2^9	512	—
2^10	1,024	1 KB (kilobyte)
2^11	2,048	—
2^12	4,096	Memory page size
2^13	8,192	—
2^14	16,384	—
2^15	32,768	Signed 16-bit max (32,767)
2^16	65,536	Unsigned 16-bit max (65,535)

The Conversion Method

Binary to decimal conversion is straightforward once you see the pattern. Each bit position has a value that doubles as you move left.

1. Write out the binary number and label each bit position from right to left, starting at 0
2. Multiply each bit (0 or 1) by 2 raised to its position number
3. Add all the results together — that is your decimal value

Example 1: Convert 1101 to decimal

Positions (right to left): bit 0 = 1, bit 1 = 0, bit 2 = 1, bit 3 = 1

• (1 x 2^3) = 1 x 8 = 8
• (1 x 2^2) = 1 x 4 = 4
• (0 x 2^1) = 0 x 2 = 0
• (1 x 2^0) = 1 x 1 = 1

8 + 4 + 0 + 1 = 13. Binary 1101 = decimal 13.

Example 2: Convert 10110 to decimal

• (1 x 2^4) = 16
• (0 x 2^3) = 0
• (1 x 2^2) = 4
• (1 x 2^1) = 2
• (0 x 2^0) = 0

16 + 0 + 4 + 2 + 0 = 22. Binary 10110 = decimal 22.

Example 3: Convert 11111111 to decimal

All eight bits are 1, so add all powers of 2 from 2^0 through 2^7:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the maximum value for one byte.

Why Computers Use Binary

Digital computers are built from billions of transistors. Each transistor is a tiny switch that is either on or off — there is no "half on." This two-state nature maps perfectly to binary: on = 1, off = 0.

Engineers tried building computers with more states (ternary computers use three states), but two-state circuits are dramatically simpler, cheaper, and more reliable. When you have billions of components on a chip, simplicity wins. That is why every modern computer, phone, tablet, and smart device uses binary at the hardware level.

Everything you see on your screen right now — this text, the colors, the layout — is stored and processed as binary numbers deep down. A letter "A" is stored as 01000001. The color white is stored as 11111111 11111111 11111111 (255, 255, 255 in RGB).

Common Binary Values Every Developer Should Know

• 8-bit maximum (255) — 11111111. One byte can hold values 0-255. This is why RGB colors, character codes, and many protocol fields max out at 255.
• 16-bit maximum (65,535) — 1111111111111111. TCP/UDP port numbers range from 0 to 65,535 because port fields are 16 bits wide.
• 32-bit maximum (~4.29 billion) — 32 ones in a row. This is why IPv4 addresses have about 4.3 billion possible values and why older systems had a 4 GB memory limit.
• Signed vs unsigned — an 8-bit unsigned integer holds 0-255. A signed 8-bit integer uses one bit for the sign, so it holds -128 to 127. Same 8 bits, different interpretation.

Decimal to Binary — The Reverse Method

To convert decimal back to binary, repeatedly divide by 2 and track the remainders:

1. Divide the decimal number by 2
2. Write down the remainder (0 or 1)
3. Take the quotient and divide by 2 again
4. Repeat until the quotient is 0
5. Read the remainders from bottom to top — that is the binary number

Example: Convert 25 to binary

• 25 / 2 = 12 remainder 1
• 12 / 2 = 6 remainder 0
• 6 / 2 = 3 remainder 0
• 3 / 2 = 1 remainder 1
• 1 / 2 = 0 remainder 1

Reading bottom to top: 11001. Decimal 25 = binary 11001.

Binary in Real Life

Binary is not just an academic concept. You encounter it in practical computing every day:

• IP addresses — an IPv4 address like 192.168.1.1 is actually four 8-bit binary numbers: 11000000.10101000.00000001.00000001
• Subnet masks — 255.255.255.0 in binary is 11111111.11111111.11111111.00000000. The boundary between 1s and 0s defines the network/host split.
• File permissions (Unix/Linux) — chmod 755 means owner=111 (read+write+execute), group=101 (read+execute), others=101 (read+execute). Each digit is 3 bits.
• Color codes — hex color #FF5733 breaks down to R=11111111 (255), G=01010111 (87), B=00110011 (51) in binary.
• Character encoding — ASCII maps every letter, number, and symbol to a 7-bit binary number. UTF-8 extends this with variable-length encoding up to 4 bytes.

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