ECE 102 - Homework 2

Due  09/07/2017

• 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. 
• Do not use a calculator.

1. Represent   the following  decimal numbers in binary:    A= 73,  B =13, C=15
   Find  the products  A*B, B*C, and A*C
2. Consider the following  8-bit 2's complement numbers:     A=10110011     B=01110101     C=01100011
   Carry out 8-bit additions corresponding to A+B, B+C, A+C.   Identify  whether there is overflow/underflow in each case
3. Draw the truth tables for the following functions
        a)    A'+B'C
        b)   (A'+B)C
        c)   (A'+B)(A+C)
   Draw logic gate circuits to realize each of these functions using  inverters, AND gates and OR gates.
   
4. Draw circuits to realize the functions
   a)  F= A+ BC + D(B'+C')
   b)  F= (AB+B'C)(C+A')+D'
5. <sub>a) Draw the truth table for the circuit given below by applying different combinations of A ,B ,C and D values to the circuit.
   
   
   b) Write the logic expression for Z.</sub> 
6. Simplify each of the following expressions by applying one of the theorems. State the theorem used:
   a)  (A'C+B'C) +(A'C+B'C)'
   b)  A(BC+C'D) + BC + C'D
   c)  A + B + C'D(A+B)'
   d)  (AB'+CD')(AE+CD')
   e) [AB' +(C+D)' +E'F](C+D)
   f) (A'+BC)(D+E+F')' +(D+E+F')