Question

Convert the following decimal number into (a) binary and (b) Octal (SHOW ALL STEPS)

205.75

Answer 1

(a) Binary :

Theory:An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero. This is done for the integer part.But for the fractional part, we just have to multiply-by-2 and decimal carry of either "1" or "0" untill the final result equals to zero or the recursion near to a point

Number : 205.75

1)Integer part:205

Divide by 2 continously

Result: Remainder:

125 1 (LSB)

62 1

31 0

15 1

7 1

3 1

1 1

0 1 (MSB)

2)Decimal part : 0.75

Multiply with 2 continously

Result Decimal Carry

0.50 1(Decimal bit starts and goes downward)

0.0 1

Therefore.now the binary digit is (11111011.11)₂

(b) Octal :

Theory:An easy method of converting decimal to binary number equivalents is to write down the decimal number and to continually divide-by-8 (eight) to give a result and a remainder until the final result equals zero. This is done for the integer part.But for the fractional part, we just have to multiply-by-8 and decimal carry untill the final result equals to zero or the recursion near to a point

Number : 205.75

1)Integer part:205

Divide by 8 continously

Result: Remainder:

25 5 (LSB)

3 1

0 3(MSB)

2)Decimal part : 0.75

Multiply with 8 continously

Result Decimal Carry

0.00 6(Decimal bit starts and goes downward)

Therefore.now the octal digit is (315.6)8