Question

prove by MATHEMATICAL INDUCTION that the process of converting decimal to binary numbers always works

Answer 1

so by induction, any decimal number can be converted to binary

step 1; take any decimal number

step 2; divide the number by 2 and keep the remainder aside continue to step 1

step3; when no more can the number be divided considering the last number take all the remainder values from bottom up

eg

considering the value 166

166/2 r=0

83/2 r=1

41/2 r=1

20/2 r=0

10/2 r=0

5/2 r=1

2/2 r=0

1

considering 1 then take all the r values bottom to top

so the binaey equivalent of 166 is 10100110

Answer 2

step 1; take any decimal number

step 2; divide the number by 2 and keep the remainder aside. Continue to step 1

step3; when no more can the number be divided considering the last number, take all the remaining values from the bottom up

eg

considering the value of 166

166/2 r=0

83/2 r=1

41/2 r=1

20/2 r=0

10/2 r=0

5/2 r=1

2/2 r=0

1

considering 1, then take all the r values bottom to top

so the binary equivalent of 166 is 10100110