Question

1. Given A = (1111 0011 1100 0011 1100 0000 0000 0000)₂ and assuming A is a single precision IEEE-754 floating point number, what decimal value does A represent? Show A in normalized scientific notation: 1.X * 2^Y.

2. Convert (28.4)₁₀ to IEEE-754 single-precision binary.

3. Given X = (0100 0010 0000 1111 0000 0000 0000 0000)₂ and Y = (0100 0001 1010 0100 0000 0000 0000 0000)₂ in single precision IEEE-754 floating point numbers, perform the following operations. Show all of your work and express the final answer in single precision IEEE 754-floating point representation.

   1. X+Y
   2. X*Y

Hint: show each value in binary normalized scientific notation prior to performing the arithmetic. This should make following the algorithms easier.

Answer 1

Given A = (1111 0011 1100 0011 1100 0000 0000 0000)₂ and assuming A is a single precision IEEE-754 floating point number, what decimal value does A represent? Show A in normalized scientific notation: 1.X * 2^Y.

ANSWER:

The first bit is sign bit next 8 bits are exponents and last 23 bits are a fraction The 1st bit is 1: so it is negative. So next 8 bits are: 111 0011 1 => 128 64 +32+4+2+1 =>231 So next 23 bits are: 100 0011 1 100 0000 0000 0000 value = (-1)*gn * 2127 * (x) 1(as the first bit is 1) Sign e = numeric value of next 8 bits >231 x = 1 + A23 *21 + A24 *22 = 1+2 +26 + 27+28+29 - 1+0.5 0.015625 0.0078125 0.00390625 Ao*223 0.001953125 = 1.529296875 So the value would be 2231-127(1.529296875) (-1) -210 i041.529296875 (Notation of X.2 So the value is 31017825624334488167872456556544