Question

Convert 111110 base 2 to 5

Answer 1

To convert the binary number \(111110\) (base 2) to base 5, follow these steps:

1. **Convert from binary (base 2) to decimal (base 10)**.
2. **Convert from decimal (base 10) to base 5**.

### Step 1: Convert from binary to decimal

The binary number \(111110\) can be converted to decimal by calculating:

\[
1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0
\]

Calculating each term:

\[
= 1 \times 32 + 1 \times 16 + 1 \times 8 + 1 \times 4 + 1 \times 2 + 0 \times 1
\]
\[
= 32 + 16 + 8 + 4 + 2 + 0 = 62
\]

The decimal equivalent of the binary number \(111110\) is \(62\).

### Step 2: Convert from decimal to base 5

Now, we convert \(62\) from decimal to base 5 by dividing the number by 5 and keeping track of the remainders.

1. \(62 \div 5 = 12\) with a remainder of \(2\)
2. \(12 \div 5 = 2\) with a remainder of \(2\)
3. \(2 \div 5 = 0\) with a remainder of \(2\)

Reading the remainders from bottom to top, we get \(222\).

### Final Result

Thus, the binary number \(111110\) in base 2 is equivalent to \(222\) in base 5.