Part 1: Form the two's complement of the following binary numbers. Show your work or describe the method you used: 11111111 01111110 01111100 11111110

Part 2: Convert the following four twos complement binary numbers to decimal and show your work: 10111 00111 01010 111111

Part 3: Compute 1000 + 0111 as a twos complement number using four bits of precision. Show your work. What is the value of the result in decimal? How do you know?

Part 4: Convert 245 and 24 to binary. Using the subtraction rule, compute 24 - 245 in binary. Show your work for all parts of the problem. (Hint: you will need to work with more than eight bits; use nine bit numbers and fixed precision.)

Part 5: A hypothetical 12-bit computer represents floating point numbers with one sign bit, six bits of exponent in twos complement format, and five bits of significand (fraction.) That is, S EEEEEE FFFFF. The exponent represents a power of two. The fractional part is normalized and there is a no "hidden" bit; all fractional bits are explicitly stored.

First, convert the exponent and significand of the following number, separately, to decimal; show your work. (Hint: don't forget that the significand has an implied binary point.)

0 000010 10000

Now, compute the decimal value of this number using the exponent and significand from the previous part; show your work.

Note: This is an invented format, designed to make problems such as this one easy to work. Real computers use one of the IEEE 754 formats.

Part 6: Analyze the circuit below. Determine the output value, Z, and each of the intermediate values W, X, and Y. (Hint: Fill in the W column, then X and Y, then finally Z.)

A	B	W	X	Y	Z
0	0
0	1
1	0
1	1