Question

6a) (6 pts. each) Find the decimal represented by the 32-bit single precision floating point number for the hexadecimal value C47CD000.

Answer 1

32 bit single precision floating point number is divided into 3 parts.

1.Sign bit of size 1.

2.Exponent part have 8 bit.

3. 23 bits for mentissa.

To convert (C47CD000)₁₆ in decimal.

Step1: Convert (C47CD000)₁₆in binary form.

1100 0100 0111 1100 1101 0000 0000 0000.

Step 2: Here 1st bit represent sign bit.

If sign bit is 1 then number is negative.

if sign bit is 0 then number is positive.

Here 1st bit is 1 hence number is negative.

Step 3: Next 8 bit represent excess 127 exponent bit.

Convert next 8 bit into decimal form .

Convert (10001000)₂ in decimal form.

1*2^7+0*2^6+0*2^5+0*2^4+1*2^3+0*2^2+0*2^1+0*2^0=(137)₁₀

Subtract 127 from converted decimal exponent.

137-127=10.

Step 4:Denormalized last 23bits by adding 1 before 9 bit.

1.111 1100 1101 0000 0000 0000

Multiply by 2^10. By shifting decimal point towards right we get.

(1111 1100 110.10000 0000 0000)₂

Convert above binary number into decimal no.

1*2^10+1*2^9+1*2^8+1*2^7+1*2^6+1*2^5+0*2^4+0*2^3+1*2^2+1*2^1+0*2^0+1*2^-1

=1024+512+256+128+64+32+0+0+4+2+1+0.5

=(2023.5)₁₀

As the sign bit is 1 hence the no will be negative that is (-2023.5)_10.

Decimal represented by the 32-bit single precision floating point number for the hexadecimal value C47CD000 is (-2023.5)_10.