Test: Floating Point Number- 1

Booth’s algorithm is used for floating point multiplication.

0 - 100 + 100 - 1 evaluates to 57 in Booth’s coding as below:

Booth recording of a multiplier are

Therefore, option (a) gives worst performance because it contains maximum number of 1 's.

The range of the magnitude of the normalized numbers is as follows: 0.5 to (1 - 2^-23).

Therefore, after the sequence value of X and Y are 1.0 and 0.0 respectively.

0.25 x 2 = 0.50;
0.50 x 2 = 1.00
Therefore, the decimal value 0.25 is equivalent to binary 0.01.

The 2’s complement of negative numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero 
+15 = 0 1 1 1 1
The 2’s complement representation of the decimal value -15 is
-15 in 2’s complement = 10001

Sign extension is the operation, in computer arithmetic, of increasing the number of bits of a binary number while preserving the number’s sign (positive/negative) and value.

So -25 is divisible by -5 so we can say 11100111 is divisible by 11111011.

Then the floating point number represented