Find the binary equivalent of the decimal number 875.875.
A) $1101011011.111 _ { 2 }$
B) $1101101011.111 _ { 2 }$
C) $1101101011.011 _ { 2 }$
D) $1011101011.111$,
E) None of these

Question

Find the binary equivalent of the decimal number 875.875. 
A) $1101011011.111 _ { 2 }$
B) $1101101011.111 _ { 2 }$
C) $1101101011.011 _ { 2 }$
D) $1011101011.111$,
E) None of these

Quizplus · Accepted Answer

To convert the decimal number 875.875 to binary, we convert the whole number and fractional part separately. For the whole number 875, we repeatedly divide by 2 and record the remainders:875 ÷ 2 = 437 remainder 1437 ÷ 2 = 218 remainder 1218 ÷ 2 = 109 remainder 0109 ÷ 2 = 54 remainder 154 ÷ 2 = 27 remainder 027 ÷ 2 = 13 remainder 113 ÷ 2 = 6 remainder 16 ÷ 2 = 3 remainder 03 ÷ 2 = 1 remainder 11 ÷ 2 = 0 remainder 1Reading the remainders from bottom to top gives 1101101011.For the fractional part .875, we multiply by 2 until we get a whole number or a repeating pattern:.875 * 2 = 1.75 (record the 1, keep the .75).75 * 2 = 1.5 (record the 1, keep the .5).5 * 2 = 1.0 (record the 1)Putting it all together, we get 1101101011.111 for 875.875 in binary.

Find the Binary Equivalent of the Decimal Number 875 1101011011.11121101011011.111 _ { 2 }1101011011.1112​

Find the Binary Equivalent of the Decimal Number 875 $1101011011.111 _ { 2 }$