Floating Point Examples
(fraction representation)
Try checking these results at http://babbage.cs.qc.edu/courses/cs341/IEEE-754.html
0 10000001 000 0000 0000 0000 0000 0000
= +2(129-127) x 1.0
= +22
= +4
1 10000001 000 0000 0000 0000 0000 0000
= -2(129-127) x 1.0
= -22
= -4
0 10001111 000 0000 0000 0000 0000 0000
= +2(143-127) x 1.0
= +216
= +65 456
0 01111111 100 0000 0000 0000 0000 0000
= +2(127-127) x 1.1 (the
fullstop here is a binary point not a decimal point)
= +20 x 1½
= +1.5
0 01111111 110 0000 0000 0000 0000 0000
= +2(127-127) x 1.11 (the
fullstop here is a binary point not a decimal point)
= +20 x 1(½+¼)
= +1.75
0 10000001 111 0000 0000 0000 0000 0000
= +2(129-127) x 1.111 (the fullstop
here is a binary point not a decimal point)
= +22 x 1.111
= +111.1 (move the binary point two places to the right)
111.1 is 7.5 in decimal
This could have been worked out in another way
= +22 x 1.111 (in
binary)
= +4 x (
1+½+¼+⅛) (in decimal)
= + 4 + 2 +
1 + ½
= +7.5
The biggest positive number that can be represented
is
0 11111110 111 1111 1111 1111 1111 1111
= +2(254-127) x 1.111 1111 1111 1111 1111 1111
= +2127
x 1.111 1111 1111 1111 1111 1111
= +2104
x 1111 1111 1111 1111 1111 1111
= +2104(+224 – 1)
The smallest positive number that can be represented
is
0 00000001 000 0000 0000 0000 0000 0000
= +2(1-127) x 1.0
= +2(-126)
Infinity is NotaNumber or NaN
0 11111111 000 0000
0000 0000 0000 0000
11111111 is 255 in decimal
Zero is
0 00000000 000 0000
0000 0000 0000 0000