To convert the binary number \(111110\) (base 2) to base 5, follow these steps:
- Convert from binary (base 2) to decimal (base 10).
- 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.
- \(62 \div 5 = 12\) with a remainder of \(2\)
- \(12 \div 5 = 2\) with a remainder of \(2\)
- \(2 \div 5 = 0\) 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.
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