Floating point representation

Question

What is the 16 bits pattern which represent (-13.5) in normalized signed magnitude fraction . S = 1 bit , Exponent = 7 bits , Mantissa = 8 bits . Represent it in hexadecimal also.

Answer 1

Since $-13.5$ is negative number so $s = 1$

Exponent = $7$ bits, therefore bias = 63

$13.5$ in binary = $1101.1$ = $1.1011 * 2^3$

E = e + bias = $3 + 63$ = $66$ = $1000010$

We store number like

S (1bit)

E (7 bits)

M (8bits

 

1

1000010

10110000

 

$(1100001010110000)_{2}$ = $(C2B0)_{H}$

 

Comments

can u elaborate this plz

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By default explicit representation, not implicit

So , 13.5 = 1101.1 = 0.11011 * 2⁴

E= 4+64  =68 =1000100

So number is like

1 1000100 11011000

Hexadecimal= 0x(C4D8)

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Incorrect solution. Bias is 63 and not 64

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@aaaakash001 thanks for pointing out 

Answer 2

Since is -13.5 is negative number so s=1

Exponent = 7 bits So, bias  = $2^{^{n-1}} – 1$ = 63 bits, therefore bias = 63 and not 64

number 1101.1 (i.e. 13.5)  after normalization is $1.1011*e^{^{3}}$

E = e + bias = 3 + 63 = 66

S (1bit)

E (7 bits)

M (8bits

 

1

1000010

10110000

 

in hexadecimal  = (C2B0)H