To convert 19.235 to bicimals with 4 decimal places, we need to convert it from base 10 to base 2.
The whole number part of 19.235 in base 2 is obtained by repeatedly dividing the number by 2 and recording the remainders until the quotient becomes 0.
19 divided by 2 equals 9 with a remainder of 1.
9 divided by 2 equals 4 with a remainder of 1.
4 divided by 2 equals 2 with a remainder of 0.
2 divided by 2 equals 1 with a remainder of 0.
1 divided by 2 equals 0 with a remainder of 1.
Reading the remainders from bottom to top, we get the whole number part in base 2 as 10011.
For the fractional part, we multiply the fractional part by 2 and record the whole number part of the result. We repeat this process until we achieve the desired number of decimal places.
0.235 * 2 = 0.47 (whole number part is 0)
0.47 * 2 = 0.94 (whole number part is 0)
0.94 * 2 = 1.88 (whole number part is 1)
0.88 * 2 = 1.76 (whole number part is 1)
Reading the whole number parts from left to right, we get the fractional part in base 2 as 0011.
Putting it all together, the bicimal representation of 19.235 to 4 decimal places is 10011.0011.