ECE 102 - Homework 1

Due  08/31/2017

• Follow the guidelines for preparing homework solutions.
• Graded homework will be distributed during labs. Provide your name and the lab section number on top of the first page.
• Turn in solutions to all the problems.  Only few selected problems will be graded.
• Do not use a calculator.
  

1. Consider the following 8-bit binary integers:    11000010  01011011
   a) Convert the numbers to decimal 
   b) Convert the numbers to octal and then to decimal
   c) Convert the numbers to hexadecimal, and then to decimal.
   
   
2. Consider the following decimal integers: 983, 2430
   a) Convert the above numbers directly to binary
   b) Convert the numbers to octal first, and then to binary
   c) Convert the numbers to hexadecimal first and then to binary.
   
   
3. Add the following binary number pairs.  Convert to octal and repeat the addition in octal. Check to ensure your results match.
   10111100 + 01101110,  01111111+01111111.
   
   
4. Represent the following decimal numbers in binary:
           67.52,    58.132
   
   
5. Add, subtract and multiply the following binary number pairs.
   Verify answers by doing the computation after converting to decimal.
        a) 101011 and 10111   c) 110110 and 10111
   
   
6. Express each of the following as a binary number.
    a)2037₈;  b)EA3B₁₆;   c) 100100111000 (BCD);  d)3337_10.
   
   
   
7. Divide in binary. Round off the result to three fractional bits:
      a) 10111101/110
      b) 1010100101 /1101
   
   
8. Consider the decimal values A= -70,   B= -52,  C= 33,  and  D = -90.
   a) Represent A,B,C,D in 8-bit sign-magnitude, 1's complement and 2's complement notations.
        
   b) Find the values of  (A+C), (B+C), (B+D), (A-D).
      Do all the operations in two's complement arithmetic.
      Identify any overflow.    Verify your answers by converting to decimal.