Write the decimal number 1878125base10 in the normalized bin

Write the decimal number (18.78125)base10 in the normalized binary form.

Solution

0.78125*2 = 1.5625 carry 1

0.5625*2=1.125 carry 1

.125*2=0.250 carry 0

0.250*2= 0.5 carry 0

0.5*2 = 1.0 carry 1

(0.78125)₁₀ =(0.11001)₂

18/2 =9 remainder =0

9/2 = 4 remainder =1

4/2= 2 remainder =0

2/2 =1 remainder =0

1

so (18)₁₀ = (10010)₂

so (18.78125)₁₀ =(10010.11001)₂