Convert the following numbers to single-precision IEEE floating point format. Ex

Question

Convert the following numbers to single-precision IEEE floating point format. Express your answer in hexadecimal X = -23.75 HEX: Y = 0.0025 HEX: For simplicity assume a mini IEEE format where the M field is only 5 bits wide. Add the following numbers and show the result for each of the four rounding modes. X = 1.01111 x 22 and Y= 1.11001 x 2 -2 Round to + infinity: Round to 0: Round to -infinity: Round to Nearest: What are the values of the guard, round, and sticky bits of the denormalized operand in the addition above? g: r: s:

Explanation / Answer

a)

X= -10111.11

   = -17.C

Y = 0.00000000101000111101011100001010

= 0.00A3D70A3D70

b)

X = 1.01111 * 22 = 1.46875 * 4 = 5.87500

Y = 1.11001 * 22 = 1.78125 * 0.25 = 0.44531

X + Y = 6.32031

round to - = 6

round to = 7

round towards 0 = 6

round away from 0 = 7

g = 0

r = 3

s = 1

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