When turning in a homework problem, mark it with the exercise number shown in bold here. These will be the reference numbers I use in reporting back your standing on the homework.

**3.x1**: All numerals in this problem are given in six bit wide two's complement signed notation, and your answers should be too. Answer each of the following arithmetic problems, and in each also indicate whether overflow occurred, and if so, how far off the answer is.010101 + 000101 =

010101 + 001100 =

110101 + 001100 =

011010 - 111101 =

101001 - 000100 =

**3.x2**: Write down the binary representation of each of these decimal numerals, assuming the IEEE 754 single precision format.−10.25

0.75

**3.x3**: Write the 32 bits for the floating point number that results from multiplying by four the floating point number1000 1001 1010 1011 1110 0000 0000 0000

(Note that this is divided into chunks of four bits just to help you count positions more accurately. The chunks do not correspond to the logically significant portions of the representation.) Be sure to explain how you arrived at your answer.

**3.x4**: The number*x*is greater than 0.25 and less than 0.5. When its value is written as a single precision floating point numeral, seven of the bits are 1 (and so the other 25 bits are 0). Find one possible value for*x*and state it in both decimal form and as a single precision floating point numeral.

Instructor: Max Hailperin