Question

1 please

IEEE-754 Floating point conversions problems (assume 32 bit machine): 1. For IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values: a. 27.1015625 b.-1 2. For IEEE 754 single-precision floating point, what is the decimal number, whose hexadecimal representation is the following? a. 4280 0000 b. 7FE4 0000 c. 0061 0000 3. For IEEE-754 single-precision floating point practice the following problem: Suppose X and Y are representing single precision numbers as follows: X 0100 0110 1101 1000 0000 0000 0000 0000 (base 2, binary) Y 1011 1110 1110 0000 0000 0000 0000 0000 (base 2, binary) Perform the following (SHOW all your work): a) X+Y b) X*Y

Answer 1

1)
a)
27.1015625 in simple binary => 11011.0001101
so, 27.1015625 in normal binary is 11011.0001101 => 1.10110001101 * 2^4

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+4=131) => 10000011
frac bits are 10110001101000000000000

so, 27.1015625 in single-precision format is 0 10000011 10110001101000000000000
in hexadecimal it is 0x41D8D000

b)
-1.0 in simple binary => 1.0
so, -1.0 in normal binary is 1.0 => 1. * 2^0

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+0=127) => 01111111
frac bits are 00000000000000000000000

so, -1.0 in single-precision format is 1 01111111 00000000000000000000000
in hexadecimal it is 0xBF800000

c)
1.0 in simple binary => 1.0
so, 1.0 in normal binary is 1.0 => 1. * 2^0

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+0=127) => 01111111
frac bits are 00000000000000000000000

so, 1.0 in single-precision format is 0 01111111 00000000000000000000000
in hexadecimal it is 0x3F800000