**Convert -511 into a 32-bit two’s complement binary number.**

**1. Convert -511 into a 32-bit two’s complement binary number.**

2. Given the bit pattern A=1000 0000 1100 1010 0100 0000 0000 0000

3. Given *x *= 0000 0000 0000 0000 0000 0000 0010 0101(*two*) and

*y *= 0000 0000 0000 0000 0000 0000 1111 0110(*two*) in two’s complement binary representation, show all of your work for the following:

a. *x *× *y *using standard shift and add method.

b. Using Booth’s algorithm. Which method is more efficient in this case?

**4. What is the IEEE-754 single-precision binary representation of the floating point number 63.25?**

5. Given *x *= 0011 1111 1011 1100 0000 0000 0000 0000(*two*) and

*y *= 0011 1001 1111 1000 0000 0000 0000 0000(*two*) in single precision IEEE 754-floating point numbers, perform the following operations. Show all of your work and express the final answer in single precision IEEE 754-floating point representation.

a. *x *+ *y*

b. *x *× *y*

**Category:**Mathematics, General Mathematics

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