The IEEE Format for storing float (single

precision)data type

Use the “enter” key to proceed through the show.

Converting a decimal value

with a fractional portion

to binary

Watch the Video first:

Click on this link: Base-10 to Base-2 Conversion: Method

Then, continue to view this show.

Converting a binary value with a fractional

portion to

floating point notation(for storing in IEEE standard for single precision float data type)

Let’s use as an example: 1011.00112

Step 1: Move the radix point to the right of the of the leftmost significant digit, and count the number of places the radix point moved.

1011.00112

IT MOVED 3 PLACES TO THE LEFT IN THIS CASE.

Let’s use as an example: 1011.00112

Step 2: Determine the exponent.

It is the number of positions the radix point moved (in this case to the left - creating a positive exponent)

Now the value looks like this:

1.0110011 x 23B

AS

E

2 V

ALU

E

NUMBER OF PLACES RADIX POINT MOVED LEFT FROM INITIAL

POSITION

Let’s use as an example: 1011.00112

The value in floating point notation:

1.0110011 x 23

can now be manipulated for storage in the 32 bit (single precision) register.

SIDE NOTE # 1

The binary value: 0.0001012

would require the radix point to be moved to the RIGHT (4 places)

thus creating a NEGATIVE exponent

End result: 1.01 x 2-4

Storing a binary value represented in

floating point notationin a 32 bit

float register

(for storing in IEEE standard for single precision float data type)

The Float Register:1s

t bi

t st

ores

the

sig

n of

the

val

ue0

for

posi

tive,

1 f

or n

egat

ive

The Example:

1.0110011 x 23

0

The example is a positive value, so zero (0) is placed in the sign bit.

The Float Register:

next

8 b

its s

tore

the

exp

onen

t w

ith

a “b

ias”

app

lied.

(bits

2 -

9)

The Example:

1.0110011 x 23

0

The exponent of the example is 3.Since exponents can be positive or

negative, a bias is used.In other words the 256 possible exponent values

that can be stored in 8 bits (28 = 256)in simplified terms must be split in half,

half for positive exponents and half for negative exponents.

So, add 127 to the exponent and store its binary value3+ 127 = 13010

13010 = 100000102

10000010

Important!You must use all 8 bits.Thus, the value may require “padding” of leading zeros

(on the left).

More information on the bias and special

cases to follow in a video near the end of this show.

The Float Register:

last

23

bits

sto

re t

he m

antis

sa(b

its 1

0 -

32)

The Example:

1.0110011 x 23

0

The mantissa of the example is .o110011.

Yikes! Where did the 1 to the LEFT of the radix point go?

It is IMPLIED but not stored (saving space). Thus the precision of the value is 24

bits even though only 23 bits are stored.

So, only the portion of the value to the right of the radix point is

stored.

10000010

Important!You must use all 23 bits.

Thus, the value may require “padding” of trailing zeros

(on the right).

01100110000000000000000

Watch these videos to reinforce the concept…

IEEE 754 Floating Point Representation Part I

IEEE 754 Floating Point Representation Part II

(This video contains more on the bias.)

Then, continue the show…

Watch this Video to see an alternate method

for converting decimal values to

binary…

alternate method

The end.Questions?

Please e-mail me.(f-porps@neiu.edu)

Works Cited:

"Base-10 to Base-2 Conversion: Method." YouTube. 13 Feb. 2013. <http://www.youtube.com/watch?v=96MJVzVKoIE>.

"IEEE-754 Single Precision Representation: Part 1 of 2 ." YouTube. 13 Feb. 2013. <http://www.youtube.com/watch?v=atlaD7M30sY>.

"IEEE-754 Single Precision Representation: Part 2 of 2 ." YouTube. 13 Feb. 2013. <http://www.youtube.com/watch?feature=endscreen&NR=1&v=b7u_oFlG4_M>.

"Base-10 to Base-2 Conversion: Another Method ." YouTube. 13 Feb. 2013. <http://www.youtube.com/watch?annotation_id=annotation_804930&feature=iv&src_vid=96MJVzVKoIE&v=hXhz80U8Fjo>.