In this problem, assume integers and floats are both 9 bits. The floating point

Question

In this problem, assume integers and floats are both 9 bits.  The floating point representation consists of     1 sign bit    4 bits biased exponent, bias = 7, E_min = -6, E_max = 7    4 bits fraction    Exponents with all 0's or all 1's follow a convention analogous      to the IEEE standard    The rounding mode is IEEE nearest  Give answers to the following problems in the floating point representation just presented.  a)  The smallest possible positive number b)  The largest possible positive number (not infinity) c)  The smallest number greater than 1 d)  The largest number less than 1 e)  Integer 001101010 f)  Product of floating point numbers: 010100100 x 011110000 g)  Product of floating point numbers: 010100100 x 001010001 h)  Difference of floating point numbers:  010000011 - 001110111 i)  Sum of floating point numbers: 010000000 + 000111111 

Explanation / Answer

a.) Smallest possible positive number (denormalized) = 2^-11

Smallest possible positive number (in normal form) = 2^-6

b.) Largest possible positive number = 1.1111 (in binary) * 2^7 = 2^7 (1 + 1/2 + 1/4 + 1/8 + 1/16) = 2^7 (31/16) = 31 * 8 = 248

c.) Smallest number greater than 1 = 1.0001 (in binary) * 2^0 = 1.0625 (in decimal)

d.) Largest number less than 1 = 0.1111 * 2^0 = 0.9375 (in decimal)

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.