Question

Show the IEEE 754 binary representation of the number -0.25(subscript)ten in single

and double precision.

List all the

steps required to get the single and double precision.

Answer 1

Solution:

Given,

=>IEEE 754 floating point representation is used.

=>Decimal number = -0.25

(a)

Explanation:

Single precision frame format:

Sign(S)

Exponent(E)

Mantissa(M)

      1 bit                         8 bits                                  23 bits

=>Normalized form = (-1)^S*(1.M)*2^(E-127)

Converting decimal number to binary from:

=>(-0.25)₁₀ = (-0.01)₂

Converting number in normalized form:

=>Number in normalized form = (-1)^1*(1.00000000000000000000000)*2^-2

=>S = 1

=>E - 127 = -2

=>E = 125 in decimal

=>E = 01111101 in binary

=>M = 00000000000000000000000

=>Hence number single precision = 10111110100000000000000000000000

(b)

Explanation:

Double precision frame format:

Sign(S)

Exponent(E)

Mantissa(M)

       1 bit                         11 bits                                  52 bits

=>Normalized form = (-1)^S*(1.M)*2^(E - 1023)

=>(-0.25)₁₀ = (-0.01)₂

Converting number in normalized form:

=>Number in normalized form = (-1)^1*(1.0000000000000000000000000000000000000000000000000000)*2^-2

=>S = 1

=>E - 1023 = -2

=>E = 1021 in decimal

=>E = 01111111101 in binary

=>M = 0000000000000000000000000000000000000000000000000000

=>Hence number in double precision = 1011111111010000000000000000000000000000000000000000000000000000

I have explained each and every part with the help of statements attached to the answer above.