💻 Free CS Tool

Free Number System Converter — Binary, Octal, Decimal & Hex

Convert any number between Binary, Octal, Decimal and Hexadecimal instantly. Get full step-by-step working shown for every conversion. Perfect for computer science homework, digital electronics, and programming. No sign-up, completely free.

✓ Binary ↔ Decimal ✓ Binary ↔ Octal ✓ Binary ↔ Hex ✓ Decimal ↔ Octal ✓ Decimal ↔ Hex ✓ All-in-One Converter

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Number System Converter — Select conversion type below

Enter any number in any base — all conversions shown instantly

Your Number

Base: Decimal (10) Binary (2) Octal (8) Hex (16)

Quick examples: Decimal 255 = Binary 11111111 = Octal 377 = Hex FF | Decimal 10 = Binary 1010 = Octal 12 = Hex A

Binary (Base 2) → Decimal | Octal | Hexadecimal

Binary Number (0s and 1s only)

Decimal (Base 10) → Binary | Octal | Hexadecimal

Decimal Number

Octal (Base 8) → Binary | Decimal | Hexadecimal

Octal Number (digits 0–7 only)

Hexadecimal (Base 16) → Binary | Octal | Decimal

Hexadecimal Number (0–9 and A–F)

ASCII Character ↔ Decimal ↔ Binary ↔ Hex

Character or ASCII Code

ASCII tip: Enter a single character (A, a, 0, @) to get its codes, OR enter a decimal number (65) to get the character. Uppercase A=65, a=97, 0=48, space=32.

Step by Step

How to convert between number systems

How to convert Binary to Decimal

Multiply each binary digit by 2 raised to its position power (starting from 0 on the right), then add all results.

Decimal = Σ (bit × 2^position)

Example: Convert Binary 11001101 to Decimal 1×2⁷ + 1×2⁶ + 0×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 128 + 64 + 0 + 0 + 8 + 4 + 0 + 1 = 205

How to convert Decimal to Binary

Divide the decimal number by 2 repeatedly, recording the remainder each time. Read the remainders from bottom to top.

Divide by 2 → record remainder → read bottom to top

Example: Convert Decimal 13 to Binary 13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Read remainders bottom to top → Binary = 1101

How to convert Binary to Hexadecimal

Group binary digits into groups of 4 from the right. Convert each group to its hex equivalent.

Group into 4 bits → convert each group to hex digit

Example: Convert Binary 11111111 to Hex Group: 1111 | 1111
1111 = 15 = F
1111 = 15 = F
Result = FF

How to convert Decimal to Hexadecimal

Divide the number by 16 repeatedly. Remainders 10–15 become A–F. Read remainders from bottom to top.

Divide by 16 → remainders 10=A, 11=B, 12=C, 13=D, 14=E, 15=F

Example: Convert Decimal 255 to Hex 255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Read bottom to top → Hex = FF

Common number conversions reference table

Decimal	Binary	Octal	Hex
0	0000	0	0
1	0001	1	1
2	0010	2	2
4	0100	4	4
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
64	1000000	100	40
128	10000000	200	80
255	11111111	377	FF
256	100000000	400	100

Reference

The four number systems explained

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Decimal

Base 10

Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Example: 255, 1024, 42

The number system humans use in everyday life. Each position represents a power of 10.

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Binary

Base 2

Digits: 0, 1 only

Example: 11111111, 1010, 1101

Used by computers and digital electronics. Each digit is a "bit". 8 bits = 1 byte. All computer data is ultimately binary.

8️⃣

Octal

Base 8

Digits: 0, 1, 2, 3, 4, 5, 6, 7

Example: 377, 17, 644

Used in Unix file permissions (chmod 755). Each octal digit represents exactly 3 binary bits.

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Hexadecimal

Base 16

Digits: 0–9 and A, B, C, D, E, F

Example: FF, 1A3F, 0x2563EB

Used in programming, memory addresses, HTML color codes (#FFFFFF), and MAC addresses. Each hex digit = 4 binary bits.

Hexadecimal digit reference

Decimal	Binary	Hex	Decimal	Binary	Hex
0	0000	0	8	1000	8
1	0001	1	9	1001	9
2	0010	2	10	1010	A
3	0011	3	11	1011	B
4	0100	4	12	1100	C
5	0101	5	13	1101	D
6	0110	6	14	1110	E
7	0111	7	15	1111	F

Why Us

Why use this number system converter?

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Instant all-in-one

Enter any number in any base — get Binary, Octal, Decimal and Hex all at once instantly.

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Steps always shown

Every conversion shows the full step-by-step working — division method, positional method — so you learn the technique.

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One-click copy

Click any result card to instantly copy the value to clipboard — no selecting, no right-clicking needed.

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ASCII converter

Convert any character to its ASCII decimal, binary, hex and octal codes — and reverse too.

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Input validation

The tool validates your input — flags invalid binary (non 0/1), invalid octal (8/9), invalid hex automatically.

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100% free, no sign-up

No account, no email, no hidden limits. Works on any device — built for CS students who need fast answers.

FAQ

Frequently asked questions about number systems

Multiply each binary digit by 2 raised to its position (starting from 0 at the right), then add all results. Example: 1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8 + 4 + 0 + 1 = 13. Our tool shows this full positional breakdown step by step for every conversion.

Divide the decimal number by 2 repeatedly, recording the remainder each time. Read the remainders from bottom to top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Read remainders bottom to top: 1101. So decimal 13 = binary 1101.

Group the binary digits into groups of 4 from the right (add leading zeros if needed). Convert each group to its hexadecimal equivalent. Example: 11111111 → 1111 | 1111 → F | F → FF. The hex digits 0–9 map directly, and 10=A, 11=B, 12=C, 13=D, 14=E, 15=F.

Group the binary digits into groups of 3 from the right (add leading zeros if needed). Convert each group to its octal digit. Example: 11111111 → 011 | 111 | 111 → 3 | 7 | 7 → 377. Each octal digit represents exactly 3 binary bits, making this conversion very straightforward.

Hexadecimal is used in: (1) HTML/CSS color codes — #FFFFFF is white, #000000 is black. (2) Memory addresses in programming — 0x1A3F. (3) MAC addresses — 00:1A:2B:3C:4D:5E. (4) Debugging assembly and machine code. (5) IPv6 addresses. Hex is preferred because each hex digit represents exactly 4 binary bits, making it compact and easy to work with.

Binary (base 2) is the fundamental language of all computers and digital electronics. Every piece of data — text, images, audio, video, programs — is ultimately stored as binary. A single binary digit is called a bit. 8 bits = 1 byte. Computers use binary because electronic circuits have two natural states: on (1) and off (0).

255 in binary is 11111111. This is significant in computing because it is the maximum value that can be stored in 1 byte (8 bits). In hexadecimal, 255 = FF. In octal, 255 = 377. This is why IP addresses max out at 255 per octet (e.g. 192.168.1.255) and why RGB color values range from 0 to 255.

Multiply each octal digit by 8 raised to its position (starting from 0 at the right), then add all results. Example: Octal 377 = 3×8² + 7×8¹ + 7×8⁰ = 3×64 + 7×8 + 7×1 = 192 + 56 + 7 = 255.

The ASCII value of uppercase A is 65 in decimal, 01000001 in binary, 41 in hexadecimal, and 101 in octal. Lowercase 'a' is 97. The ASCII table maps 128 characters (0–127) to their numeric codes. Use our ASCII converter tab to instantly look up any character or code.