1. To fully understand operation on ALU, you require to have a good knowledge of representation of positive, negative and fractional numbers in binary number system. In addition, you should understand how the mathematical operations (such as addition and subtraction) are performed on the number system. This lab work will assist you to become proficient with signed-magnitude and twos complement representations and mathematical operations on those representations. All students should able to perform the following tasks manually (without using a computer or calculator).

The following table shows decimal numbers. Convert each decimal number to signed-representation and twos complement equivalent manually in 8 bits (you can use calculator or computer to convert from decimal to binary):

Decimal Number	Signed Representation	Twos Complement Representation
49
-49
14
-14
+127
-127
128
-128

2. Convert the following decimal to 2s Complement 8 bit binary. Using twos complement and addition, calculate the result of the following:

1. 63 + 49 =

2. 59 37 =

3. -34 22 =

Comment about the validity of the result. Convert the results back to decimal to verify your answer.

3. Convert the following real base 10 numbers into IEE754 floating point number format...

45.25₁₀

-128.0625₁₀

21.3₁₀ (note this is tricky!)

4. Convert the following numbers from IEEE754 floating point format to decimal real numbers

0x8B49 0000