Single Precision

Question

The decimal value of 0.005 in single precision floating point format is __________________

Comments

0   01111011   10011001100110011001100 ???

---

how??

---

0.005 already is in decimal, right?

---

0 01110111 01000111101011100001010

(-1)^s x 0.M x 2^E-127  (Implicit Normalization)

Multiply 0.005 by powers of 2 till you get 1 on left of point.

0.005 * 2 = 0.01

0.005 * 2² = 0.02

..... 0.005 * 2⁸ = 1.28

Now, 0.005 = 1.28 * 2^-8 

Exponent = 127 - 8 = 119 = 01110111

Now convert, 0.28 into binary with usual method

0.28 x 2 = 0.56        0

0.56 x 2 = 1.12        1

0.12 x 2 = 0.24        0

0.24 x 2 = 0.48        0

.

.

You will get 01000111101011100001010

I am aware of this method. 

I calculated the entire string online on 

https://www.h-schmidt.net/FloatConverter/IEEE754.html

:p

---

0x3BA3D60A

---

0 01110111 00011100
what's the correct ans
edit: i solve taking this as standard (-1)^s  (1.M)*2^E-127 where M= mantissa and E = exponent
so 0,005 is same as 1.28*2^-8 

---

@nitish

I also getting different ans

can u explain?

Answer 1

0.005

To calculate its binary equivalent

0.005 x 2	0
0.01 x 2	0
0.02 x 2	0
0.04 x 2	0
0.08 x 2	0
0.16 x 2	0
0.32 x 2	0
0.64 x 2	1
0.28 x 2	0
0.56 x 2	1
0.12 x 2	0
0.24 x 2	0
0.48 x 2	0
0.96 x 2	1
0.92 x 2	1
0.84 x 2	1
0.68 x 2	1
0.36 x 2	0
0.72 x 2	1
0.44 x 2	0
0.88 x 2	1
0.76 x 2	1
0.44 x 2	0
0.88 x 2	1
0.76 x 2	1
0.52 x 2	1
0.04 x 2	REPEAT

Binary Equivalent of 0.005 = 00000001010001111010111

also can be written as 1.010001111010111 x 2^-8

Hence in IEEE single precision (exponent) = 127-8 = 119 = 01110111

Mantissa = 01000111101011100001010 (23 bits)

Sign Bit(1)	Exponent(8)	Fraction(23)
0	01110111	01000111101011100001010

Comments

@Mk Utkarsh

As we know that the given number is a fraction why cant we go like Exponent=0 and Mantissa<>0 (not equal to zero) 

Answer 2

We have to expend mantisa upto 23 bits .