Floating Point Computer Science Question:

Consider a 9-bit floating-point representation based on the IEEE floating-point format, with one sign bit, four exponent bits (k = 4), and four fraction bits (n = 4). The exponent bias is 2^(41)1 = 7. In this problem you need to multiply 2 floating point numbers. The algorithm is outlined at each step. Assuming the given 9-bit IEEE floating-point format, multiply X = 29 and Y = 0.15625.

Part 1)

1) First covert X and Y to their bit representations. (E.g.: "011100010")

X= ___

Y=____

Part 2) Using the binary representations convert X and Y to scientific form--- i.e., express these values as 1.(mantissa_part)* 2 ^(exponent)

X=1.____ *2^______

Y=1._____*2^_______

Part 3) Add the two exponents from part 2, and write the answer as a decimal

Y=_________

Part 4) Multiply the two mantissas (not just mantissa_part !) of X and Y from step 2 together--- give the result of just that multiplication below.

The first blank below is the bit pattern of the result before the decimal point. Please include the double quotation marks and no spaces. For second blank, please specify the bit pattern within double quotation marks and without a space

Z=(X*Y)= ______ . _________ *2^(exponent from previous step)

Part 5) If the result before the decimal point is greater than 1, adjust the mantissa and exponent so that it is.

Z= 1.____ * 2^_______

Part 6) To get the new sign bit, add the 2 original sign bits together, divide by 2 and take the remainder (sum of sign bits mod 2).

(solution is zero or 1)

Part 7) Convert Z to 9-bit floating point IEEE format. To store result Z in 9-bit IEEE binary floating point representation, it needs to be rounded using round to even mode.

Z=_____