11-11-2016, 10:51 AM

Assignment No. 01

Semester: Fall 2016

Digital Logic Design – CS302

Topics Covered: Number systems to

Boolean Algebra & Logic Simplification

Question No. 01 5 Marks

In the binary number system, we represent numeric values using two different symbols which is typically 0 and 1. Suppose we have a tertiary number system, which consists of three different symbols i.e. 0, 1 and 2. You have to perform the following operation defined in a given expression where we have to subtract a tertiary number from a decimal number and have to express the output in a binary number system.

(576)10 – (110002)3 = (_?_)2Solution:

As you cannot perform any operation on two numbers that are on different Number System. So to perform the subtraction you need to convert the numbers to any one of the Binary, Tertiary or Decimal number systems. You can do so by Sum-Of-Weight Method that is explained in the handouts.

Lets suppose you convert the tertiary number into decimal and then perform the subtraction, you will see that the tertiary number is actually 326 in decimal. After subtracting, the answer will be 250. Now you can convert this number into binary to give your final answer.

The binary equivalent of 250 in Decimal is "11111010".

Question No. 02 (a) 7 Marks

Suppose we have a digital circuit expressed through the following truth table. You have to write simplified Boolean expression using Boolean Algebra.

Note: You have to write the Boolean Algebra Rule name for each simplification step.

Solution:

For this you first need to make a Boolean expression from the given Truth Table. You can do so by using any of the two methods in Lecture 8-9 of CS302 handouts, namely SOP and POS. After you have the Boolean expression you can simplify it using Boolean Algebra Rules and Laws in the Lecture 9 from Handouts of CS302. Do write all the rules that you use for simplification otherwise you might lose some score in the result.

The final simplified expression should be "~B^~C v ~A^B^D".

Question No. 02 (b) 8 Marks

Draw the circuit diagram for the simplified Boolean expression obtained from Question No. 02 (a).

Solution:

This one is quite easy after you have the simplified Boolean expression. You can also use any tool to create the Circuit diagram and Insert Image of the diagram in the assignment solution file.

If you have any questions feel free to comment below.