Need help with Binary fractions (fixed) to Decimal notation

I know the traditional way to convert binary fractions (fixed) to decimal notation. The traditional way is below:

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[-A-] Traditional technique for converting decimal number 0.42

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step 1: 0.47 * 2 = 0.94 ; store integral part: 0

step 2: 0.94 * 2 = 1.88 ; store integral part: 1

step 3: 0.88 * 2 = 1.76 ; store integral part: 1

step 4: 0.76 * 2 = 1.52 ; store integral part: 1

step 5: 0.52 * 2 = 1.04 ; store integral part: 1

[-B-]final answer: 0.01111......

question: Can I get the final answer [-B-] using shift operation ? I am looking for something similar to Double Dabble. I don't want to use [-A-] because I'm trying to avoid the Multiplication core in an FPGA. Multiplication core just takes extra clock cycles for each multiplication operation and I'd like to avoid that.

[-C-] Summary:

1. Decimal/BCD (whole) --- > Binary : use Reverse Double Dabble.

2. Decimal/BCD (fraction) --- > Binary : ????? (I don't want to use [-A-])

3. Binary(whole) --- > Decimal/BCD : use Double Dabble

4. Binary(fraction) --- > Decimal/BCD : use Reverse Double Dabble.

For [-C-].2, I'm trying to find/come up with a technique similar to [-C-].1, [-C-].3, and [-C-].4. Any suggestions?