Convert Binary to Base 3

Convert Binary (bin) to Base 3 (base 3) instantly and accurately.

Selected Binary (bin) - available characters: 0, 1

Conversion Formula

Step-by-step example using the value 42 (decimal):

Convert Binary (base 2) → Base 3 (base 3)

Step 1: Expand each digit of 101010 (bin) by position:

        1 × 2^5 = 32
        0 × 2^4 =  0
        1 × 2^3 =  8
        0 × 2^2 =  0
        1 × 2^1 =  2
        0 × 2^0 =  0
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 3 repeatedly (read remainders upward):

        42 ÷ 3 = 14  r 0
        14 ÷ 3 =  4  r 2
         4 ÷ 3 =  1  r 1
         1 ÷ 3 =  0  r 1
        Read remainders upward: 1120

────────────────────────────
Result:  101010 (bin) = 1120 (base 3)

About Binary

Binary (base 2) is the foundational numeral system of all digital electronics, using only 0 and 1. Each position represents a power of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8. Leibniz formalised it in 1679; Shannon applied Boolean logic to circuits in 1948. 8 bits = 1 byte (256 values) - the fundamental unit in every CPU from the 8080 to ARM Cortex-X. Every integer, float, character, pixel, and instruction in any digital device is ultimately binary. Conversion: decimal 42 = 32+8+2 = 2⁵+2³+2¹ = 101010₂.

About Base 3

Ternary (base 3) uses digits 0, 1, 2. Each position is a power of 3: 3⁰=1, 3¹=3, 3²=9, 3³=27. Balanced ternary (−1, 0, +1) represents negatives without a sign and minimises rounding error. The Soviet Setun computer (1958) was the only practical balanced-ternary machine. Ternary underlies the Cantor set and Toom-Cook multiplication. Conversion: decimal 42 = 1×27+1×9+2×3+0 = 1120₃.

Quick Reference Table

→ Full Number Base Converter