Question

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in non-standard form.

1100_0100_1001_1001_1000_0000_0000_0000

Answer 1

1 10001001 00110011000000000000000
sign bit is 1(-ve)
exp bits are 10001001
Converting 10001001 to decimal
   10001001
   => 1x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
   => 1x128+0x64+0x32+0x16+1x8+0x4+0x2+1x1
   => 128+0+0+0+8+0+0+1
   => 137
in decimal it is 137
so, exponent/bias is 137-127 = 10
frac bits are 00110011

IEEE-754 binary value is 1.frac * 2^exponent
IEEE-754 binary value is 1.00110011 * 2^10 = 10011001100

let's convert this to decimal
Converting 10011001100 to decimal
10011001100
=> 1x2^10+0x2^9+0x2^8+1x2^7+1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x1024+0x512+0x256+1x128+1x64+0x32+0x16+1x8+1x4+0x2+0x1
=> 1024+0+0+128+64+0+0+8+4+0+0
=> 1228

Answer in binary:   -10011001100
Answer in decimal:  -1228