Question

Calculate 1.666015625 x 10° (1.9760 x 104 + - 1.9744 x 10^) by hand, assuming each of the values are stored in the 16-bit half precision format IEEE 754-2008. IEEE 754-2008 contains a half precision that is only 16 bits wide. The left most bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. A hidden 1 is assumed. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.

Answer 1

1.666015625 X 10° X (1.9760 X 104 - 1.9744 x 104) (A) 1.666015625 X 10º = 1.1010101010 x 2° (B) 1.9760 X 10' = 1.0011010011 x 214 (C) -1.9744 x 104 = -1.0011010010 x 24 Exponents match, no shifting necessary (B) 1.0011010011 (C) -1.0011010010 (B+C) 0.0000000001 x 214 (B+C) 1.0000000000 x 24 Exp: 0+4 = 4 Signs both positive, result positive Fraction: (A) 1.1010101010 (B+C) x 1.0000000000 11010101010 1.10101010100000000000 AX(B+C) 1.1010101010 0000000000 Guard - 0. Round 0, sticky O: No round AX(B+C) 1.1010101010 x 2

Decimal: 26.65625

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