How real numbers can be encoded using a fixed precision binary encoding explain briefly.
Expert Answer
Sign-magnitude representation:
- The most-significant bit (msb) is the sign bit, with value of 0 representing positive integer and 1 representing negative integer.
- The remaining n-1 bits represents the magnitude (absolute value) of the integer. The absolute value of the integer is interpreted as “the magnitude of the (n-1)-bit binary pattern”.
- Example:
-
Convert 18.6875D to binary Integral Part = 18D 18/2 => quotient=9 remainder=0 9/2 => quotient=4 remainder=1 4/2 => quotient=2 remainder=0 2/2 => quotient=1 remainder=0 1/2 => quotient=0 remainder=1 (quotient=0 stop) Hence, 18D = 10010B Fractional Part = .6875D .6875*2=1.375 => whole number is 1 .375*2=0.75 => whole number is 0 .75*2=1.5 => whole number is 1 .5*2=1.0 => whole number is 1 Hence .6875D = .1011B Therefore, 18.6875D = 0 10010.1011B