#Number System

Question

For next 3 questions: Consider the following $8$ bit IEEE floating point representation.

• The most significant bit is sign bit
• The next $4$ bit $1’s$ complement exponent
• The last 3 bit for mantissa

65. What is smallest positive normalized number?

$(a)2^{-7}$   $(b)0$   $(c)2^{-6}$  $(d)1$

66.What is smallest  normalized number?

$(a)-259$   $(b)-255$   $(c)-256$  $(d)-240$

67.What is largest  normalized number?

$(a)259$   $(b)255$   $(c)256$  $(d)240$

 

I get confuse to solve this type of questions.......

Answer 1

we are storing exponent in 1's complement form so, with n bits, we can represent numbers between

-2^n-1-1 to +2^n-1-1. So, with 4 bits we can have numbers between -7 to +7(decimal of course).

Numbers will be of the form (-1)^sign *(1.Mantissa)* 2^exponent

So, the smallest positive normalized number would be, 0(+ ve sign)    1000(exponent, -7 in decimal)  000(mantissa 0 in decimal) which is +1.0 * 2^-7 (option A)

The smallest normalized number would be,   1(- ve sign)    0111(exponent, 7 in decimal)  111(mantissa 7 in decimal)

which is  -1.111*2⁷=11110000 =  -240. (option D)

Largest would be the same with opposite sign so +240.(option D).

Comments

the smallest positive normalized number would be, 0(+ ve sign)    1000(exponent, 7 in decimal)  000(mantissa 0 in decimal) which is +1.0 * 2^-7 (option A)

exponent should be -7 right? -7 in 1's complement is 1111, isn't it?

EDIT: Confused it with signed mag rep. Kindly ignore

---

Nope :) -7 in one's complement would be 1000 only.

---

Okay i confused it with signed magnitude ..sorry :P