Floating Point in Binary 1.Place Value Chart:

Converting from Base 10 to Base2 2.Base 10:7.875 Convert number to the left of decimal: The number to the right of decimal:.875 = (1 x.25) + (1 x.50) + (1 x.125) =.111 Therefore: =

Scientific Notation 3. Represent in Base 2 Scientific Notation: = x Where: is the Mantissa 0010 is the exponent* * The decimal was moved two place values to the left. Represent 2 as a 4 bit number in Base 2: 0010

Exponent Chart 4.Find your exponent on the following chart:

Expressing the float as a 32 bit number …………………………………………..0 SExponent Mantissa x Where: S is for the sign and is 1 bit Exponent is 8 bits Mantissa is 23 bits

Example: