NIMCET 2020 — Computer PYQ

CONCEPT:
Conversion steps (for the non-Fraction part):
1. Divide the number by 2.
2. Get the integer quotient for the next iteration.
3. Get the remainder for the binary digit.
4. Repeat the steps until the quotient is equal to 0 .
Conversion steps (for the Fraction part):
1. Multiply the decimal number by 2.
2. Get the result for the next iteration.
3. Get the number received before decimal for the binary digit.
4. Repeat the steps until the result is equal to1.

• Here, $234_{10}=11101010_2$  (Writing remainders from bottom to top)

• Now Convert $0.125_{10}$ to Binary:

• Here, $0.125_{10}=.001_2$ (Writing Carry from top to bottom)

• Now after combining the number and its fraction part, we get $11101010.001_2$.

• Hence, $(234.125{)}_{10}=(11101010.001{)}_2$