EE 274 Homework Assignment No. 1 (Data Representations and Coding)
Due: September 21, 2009 before class
Note: Type or neatly show ALL your work in arriving at your answers, i.e. do not just
write down your answers. This assignment requires independent work.
1. What are the 8-bit 2’s-complement and 1s’-complement representations for each of
the following decimal numbers: 25, 120, 82, -42, -6, -111?
Ans: For positive numbers, 2’s-complement and 1s’-complement are the same. On the
other hand, for negative numbers, express the number’s absolute value, flip the bits to get
the 1s’-complement. Then add 1 to the 1s’-complement to get the 2’s-complement.
2. What is the hexadecimal value of the number 1264843010?
Ans: Convert 1264843010 to 1100000011111111111011102 to get C0FFEE16.
3. Add the following pairs of hexadecimal numbers: F35B+27E6, 1B90F+C44E.
Ans: F35B+27E6 = 11B41; 1B90F+C44E = 27D5D. Or convert both addends to base 2,
perform the addition, then convert from base 2 back to base 16.
4. Why is 2’s-complement representation of a number useful in performing a subtraction
between two numbers?
Ans: B1 – B2 = B1 + (B2’-1), where (B2’-1) is the 2’s-complement representation of B2.
This way a subtraction is transformed into an addition, i.e. it can be done with an adder.
5. Show, using an n-cube of n=3, how you will come up with an error-correcting code.
How many errors can your code correct? Explain how your code works.
Ans: A code C is t-error correctable iff dm ≥ 2t+1. Thus given n=3 your code can correct
at most 1 error. It can detect at most 2 errors, since dm ≥ d+1 where d=2 and dm is 3 here.
