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The remainder of the division, by 4, is a number between 0 and 3. In the case of binary, this would maintain the last two bits of the original number.
28-bits
As quoted from Google Books, "Word size refers to the number of bits that a microprocessor can manipulate at one time."
There are 16 decimal numbers that can be represented by 4-bits.
The mantissa holds the bits which represent the number, increasing the number of bytes for the mantissa increases the number of bits for the mantissa and so increases the size of the number which can be accurately held, ie it increases the accuracy of the stored number.