# How real numbers can be encoded using a fixed precision binary encoding explain briefly.

How real numbers can be encoded using a fixed precision binary encoding explain briefly.

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```
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