Consider the positive decimal value 123456789 a Show the 32b

Consider the positive decimal value 123,456,789.

a) Show the 32-bit two’s complement representation of this value and indicate by how much the decimal value represented by the 32-bit pattern differs from decimal 123456789. b) Assuming that no rounding is used, show the 32-bit IEEE 754 single precision floating point representation of this value and indicate by how much the decimal floating value represented by the 32-bit pattern diffesr from decimal 123456789

c) If rounding is used in producing the 32-bit IEEE 754 single precision floating point representation of the value, by how much would the decimal floating value represented by the 32-bit pattern differ from decimal 123456789?

Solution

decimal value: 123456789

a) 32 bit two\'s complement representation: 00000111 01011011 11001101 00010101

b) 32 bit IEEE 754 single precision floating point representation : 01001100111010110111100110100011