Quaternary Conversion Tool

Base-4 to Binary Converter

Convert base-4 (quaternary) integers to binary instantly. Enter a base-4 value such as 121 and convert each digit directly into its corresponding 2-bit binary group with decimal verification.

✓ Base-4 Input ✓ Binary Output ✓ Direct 2-Bit Mapping ✓ Decimal Verification ✓ Free Unlimited Use

4→2

Base-4 → Binary

● Ready

Base-4 Integer

Enter a non-negative base-4 integer using only digits 0, 1, 2 and 3. Spaces are ignored.

Try:

✓ Binary Result

Ordinary base-2 representation

Decimal Value 0

Base-4 Digits 0

Binary Bits 0

Conversion Breakdown

What Is Base-4 to Binary Conversion?

Base-4 to binary conversion changes a quaternary number into an equivalent base-2 value. Since 4 = 2², every base-4 digit corresponds exactly to two binary bits.

Direct mapping: 0₄ = 00₂ 1₄ = 01₂ 2₄ = 10₂ 3₄ = 11₂

Base-4 to Binary Conversion Table

Base-4 Digit	Binary Pair
0	`00`
1	`01`
2	`10`
3	`11`

How to Convert Base-4 to Binary

1. Read the base-4 number

Verify that every digit is 0, 1, 2, or 3.

2. Process each digit

Treat each quaternary digit independently.

3. Replace 0 with 00

Base-4 digit 0 maps to binary pair 00.

4. Replace 1, 2 and 3

Use 01 for 1, 10 for 2, and 11 for 3.

5. Join the binary pairs

Keep the converted groups in the same left-to-right order.

6. Remove leading zeros

Unnecessary leading binary zeros can be removed from the integer result.

Example: Convert Base-4 22 to Binary

Base-4: 22₄ Convert each digit: 2 → 10 2 → 10 Join the binary groups: 1010₂ Therefore: 22₄ = 1010₂ Decimal check: 22₄ = 2×4 + 2 = 10 1010₂ = 10

Example: Convert Base-4 121 to Binary

Input: 121₄ Map each digit: 1 → 01 2 → 10 1 → 01 Join: 01 10 01 Remove the unnecessary leading zero: 11001₂ Therefore: 121₄ = 11001₂

Base-4 to Binary Examples

Base-4	Decimal	Binary
`0`	0	`0`
`1`	1	`1`
`2`	2	`10`
`3`	3	`11`
`10`	4	`100`
`11`	5	`101`
`12`	6	`110`
`13`	7	`111`
`20`	8	`1000`
`21`	9	`1001`
`22`	10	`1010`
`23`	11	`1011`
`30`	12	`1100`
`33`	15	`1111`
`100`	16	`10000`
`121`	25	`11001`

Why Does One Base-4 Digit Equal Two Binary Bits?

Four different two-bit binary combinations exist:

00 01 10 11 These represent exactly four values: 0, 1, 2, and 3. Because base 4 also has four possible digits, the mapping is exact.

Base-4 vs Binary

Feature	Base-4	Binary
Base	4	2
Allowed digits	0, 1, 2, 3	0, 1
Binary mapping	2 bits per digit	Native bits
Decimal 10	`22`	`1010`
Decimal 25	`121`	`11001`

Do Leading Base-4 Zeros Matter?

No. Leading zero digits do not affect the numerical value.

00121₄ = 121₄ Both convert to: 11001₂

Common Base-4 to Binary Mistakes

Using digits above 3

A valid base-4 number can contain only digits 0 through 3.

Using three-bit groups

Each base-4 digit maps to exactly two binary bits.

Converting the whole string as decimal

Base-4 digits use powers of 4, not powers of 10.

Dropping internal zeros

Only unnecessary leading zeros may be removed; internal binary zeros must remain.

Important: this calculator handles non-negative base-4 integers. Base-4 fractions can also map to binary in two-bit groups around the radix point, but fractional conversion is outside this page.

Related BinaryCon Tools

Base-4 to Binary Converter FAQs

How do you convert base 4 to binary?

Replace every base-4 digit with its two-bit binary equivalent: 0 = 00, 1 = 01, 2 = 10, and 3 = 11. Then join the binary groups.

What is base-4 3 in binary?

Base-4 digit 3 maps directly to binary 11.

What is base-4 11 in binary?

Convert each digit as 1 → 01, giving 0101. After removing the leading zero, the result is 101.

What is base-4 22 in binary?

Each 2 maps to 10, so 22₄ = 1010₂.

What is base-4 121 in binary?

Map the digits as 01 10 01. Removing the leading zero gives binary 11001.

Why does every base-4 digit use two binary bits?

Because 4 = 2², so the four possible base-4 digits correspond exactly to the four possible two-bit combinations.

What digits are valid in base 4?

Only 0, 1, 2, and 3.

Is base 4 also called quaternary?

Yes. Quaternary is another name for the base-4 numeral system.

Do I need to convert base 4 to decimal first?

No. Direct conversion is possible because each base-4 digit maps exactly to two binary bits.

Do leading zeros change the result?

No. Leading base-4 zeros do not change the numerical value.

Can this converter handle large base-4 integers?

Yes. The primary binary conversion works digit by digit without relying on a small fixed-width integer.

Does BinaryCon require registration?

No. The Base-4 to Binary Converter can be used directly without signup.