Number Base Converter

Binary to Base-4 Converter

Convert binary integers to base-4 instantly. Enter a binary value such as 11001 to group the bits in pairs, convert each pair into a base-4 digit, and see the decimal value and full conversion breakdown.

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

2→4

Binary → Base-4

● Ready

Binary Integer

Enter a non-negative binary integer using only 0 and 1. Spaces are ignored.

Try:

✓ Base-4 Result

Base-4 / quaternary representation

Decimal Value 0

Binary Bits 0

Base-4 Digits 0

Conversion Breakdown

What Is Binary to Base-4 Conversion?

Binary to base-4 conversion changes a base-2 number into its equivalent base-4 representation. Base 4 is also called the quaternary numeral system and uses the digits 0, 1, 2, and 3.

Because 4 = 2², every base-4 digit corresponds exactly to two binary bits.

Binary to Base-4 Grouping Rule

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

How to Convert Binary to Base-4

1. Start with binary

Write the binary number using only 0 and 1.

2. Group bits in pairs

Starting from the right, separate the binary number into groups of two bits.

3. Pad the left group if needed

If one bit remains, add a leading zero to make a complete pair.

4. Convert each pair

Map 00, 01, 10, and 11 to base-4 digits 0, 1, 2, and 3.

5. Keep the same order

Write each converted base-4 digit from left to right.

6. Remove unnecessary leading zero

The resulting digit sequence is the base-4 representation.

Example: Convert Binary 1010 to Base-4

Binary: 1010₂ Group into two-bit pairs: 10 10 Convert each pair: 10₂ = 2 10₂ = 2 Therefore: 1010₂ = 22₄ Decimal check: 1010₂ = 10₁₀ 22₄ = 2×4 + 2 = 10₁₀

Example: Convert Binary 11001 to Base-4

Binary: 11001 There are five bits, so add one leading zero: 011001 Group into pairs: 01 10 01 Convert: 01 = 1 10 = 2 01 = 1 Result: 121₄ Verification: 121₄ = 1×16 + 2×4 + 1 = 25 11001₂ = 25

Binary to Base-4 Conversion Table

Binary	Decimal	Base-4
`0`	0	`0`
`1`	1	`1`
`10`	2	`2`
`11`	3	`3`
`100`	4	`10`
`101`	5	`11`
`110`	6	`12`
`111`	7	`13`
`1000`	8	`20`
`1001`	9	`21`
`1010`	10	`22`
`1011`	11	`23`
`1100`	12	`30`
`1101`	13	`31`
`1110`	14	`32`
`1111`	15	`33`
`10000`	16	`100`
`11001`	25	`121`

Why Can Binary Be Converted Directly to Base-4?

Base 4 is exactly the square of base 2:

4 = 2² Therefore every base-4 digit represents exactly two binary positions. This makes direct grouping possible without first converting the number to decimal.

Base-4 Place Values

Power	Value
4⁰	1
4¹	4
4²	16
4³	64
4⁴	256
4⁵	1024

Binary vs Base-4

Feature	Binary	Base-4
Base	2	4
Allowed digits	0, 1	0, 1, 2, 3
Bits per base-4 digit	—	2 binary bits
Decimal 10	`1010`	`22`
Decimal 25	`11001`	`121`

What If the Binary Bit Count Is Odd?

If the binary number contains an odd number of bits, add one zero to the left before making pairs.

Binary: 101 Pad: 0101 Group: 01 01 Convert: 11₄

Adding a leading zero does not change the numerical value.

Common Binary to Base-4 Mistakes

Grouping from the left incorrectly

For integers, start grouping from the right side.

Using groups of four bits

Base 4 corresponds to two binary bits per digit, not four.

Using digit 4 in base-4

Base-4 digits are limited to 0, 1, 2, and 3.

Forgetting left-side padding

An incomplete leftmost pair can be padded with a leading zero.

Important: this calculator is designed for non-negative binary integers. Binary fractions can also be grouped in pairs around the binary point, but fractional conversion is outside this page’s scope.

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Binary to Base-4 Converter FAQs

How do you convert binary to base 4?

Group the binary digits into pairs from the right. Convert 00, 01, 10, and 11 to base-4 digits 0, 1, 2, and 3.

Why are binary digits grouped in pairs?

Because 4 = 2², so exactly two binary bits correspond to one base-4 digit.

What is binary 11 in base 4?

Binary 11 equals decimal 3, so its base-4 representation is 3.

What is binary 101 in base 4?

Pad it as 0101, group it as 01 01, and convert each pair to 1. The result is 11₄.

What is binary 1010 in base 4?

Group it as 10 10. Each pair equals base-4 digit 2, so the result is 22₄.

What is binary 11001 in base 4?

Pad it to 011001, group it as 01 10 01, and convert to 121₄.

What digits are valid in base 4?

Base 4 uses only 0, 1, 2, and 3.

Is base 4 called quaternary?

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

Do I have to convert binary to decimal first?

No. Because base 4 is a power of 2, binary integers can be converted directly by grouping bits into pairs.

What happens when there is an odd number of binary bits?

Add a leading zero so the bits can be divided into complete two-bit groups.

Do leading binary zeros affect the result?

No. Leading zeros do not change the numerical value.

Does BinaryCon require registration?

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