1. Floating Point in Binary 1.Place Value Chart: 8421.25.50.125 23232 2121 2020 2 -1 2 -2 2 -3

2. Converting from Base 10 to Base2 2.Base 10:7.875 Convert number to the left of decimal: 111.875 The number to the right of decimal:.875 = (1 x.25) + (1 x.50) + (1 x.125) =.111 Therefore: 7.875 = 111.111

3. Scientific Notation 3. Represent 111.111 in Base 2 Scientific Notation: 111.111 = 1.11111x2 0010 Where:.11111 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

4. Exponent Chart 4.Find your exponent on the following chart: 31000 0010 21000 0001 11000 0000 00111 1111 0111 1110 -20111 1101

5. Expressing the float as a 32 bit number 01000 0001111110…………………………………………..0 SExponent Mantissa 1.11111x2 0010 Where: S is for the sign and is 1 bit Exponent is 8 bits Mantissa is 23 bits

6. Example: 5.125 2.75