$35.00
Description
Problem 1:
Simplify the following equations using Boolean theorems. Check the correctness using a truth table and a KMap. (3 points each for the Boolean simplifications, 1 point for the truth table, 3 points for the Kmap, 3 point for the resultant circuit)

= +

= ++( + )
Problem 2:
Write the sum of products canonical representation (minterms) for each of the following truth tables. Y is the output of the circuits.

0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
Problem 3:
Minimize each of the circuits in Problem 2 and implement them using a simple combinational circuit using twoinput AND and OR gates, and/or a NOT gate.
Problem 4:
Design the simplest sum of products circuit that implements: _{ !}, _{!}, _{! } = (0,1,2,3,4,6,7). Use Boolean algebra to simplify the function and confirm your solution using KMaps.
Problem 5:
Consider the following truth table:
Show its sum of products (SoP) and product of sums (PoS). Also, use Boolean algebra to find the minimumcost SoP form.
Consider the following truth table:

_{!}
_{!}
_{!}
( _{!}, _{!}, _{!})
0
0
0
1
0
0
1
×
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
×
1
1
0
0
1
1
0
0
Use KMaps to design the simplest sum of products circuit.
Problem 6:
Find a minimal Boolean Equation for the truth table given below. Remember to take advantage of the don’t care entries. Draw the resultant circuit.

0
0
0
0
×
0
0
0
1
×
0
0
1
0
×
0
0
1
1
0
0
1
0
0
0
0
1
0
1
×
0
1
1
0
0
0
1
1
1
×
1
0
0
0
1
1
0
0
1
0
1
0
1
0
×
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1

1
1
0
×
1
1
1
1
1
Problem 7:
Consider the following circuit. What is its truth table?
What is the minimalcost expression for this true table? Find the simplest SoP and confirm your solution using KMaps.
Problem 8:
The following circuit (with NOT and 2input AND gates) implements the 24 decoder.
Design a 38 decoder circuit with NOT and 2input AND gates. How many gates (NOT and 2input AND gates) are needed to build the n2^{n} decoder?
Problem 9:
Give the Boolean expression for the function performed by the following circuit:
Problem 10:
Implement the following truth table as described below:

0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1

Using a 3:8 decoder and one other logic gate

Using a 8:1 multiplexer

Using a 4:1 multiplexer and one inverter

A 2:1 multiplexer and two other logic gates
Problem 11:
Identify the Boolean equation performed by the circuit below and minimize the circuit and implement it using simple gates.
Problem 12:
Design a 4to16 decoder using five 2to4 decoder
Problem 13:
Design a 32to1 multiplexer (MUX) using

8to1 MUX and 2to4 decoders.

4to1 MUX and 2to4 decoders.
Problem 14:
Given a 3input Boolean expression _{ !}, _{!}, _{! } = (0,2,4,6,7).

Implement this expression using only 24 decoders and OR gates.

Implement this expression using only 41 MUX.
Problem 15:
Implement the function _{ !}, _{!}, _{!}, _{!}, _{! } = _{! ! ! !} + _{! !} + _{! !} + _{! !} + _{! ! !} by using a 4to1 multiplexer and as few other gates as possible.
Consider the Boolean function _{ !}, _{!}, _{! } = _{! !} + _{! !} + _{! ! !}.

Use a 3to 8 decoder plus logic gates to implement this function.

Use an 8input multiplexer to implement this function.
Problem 17:
Gray codes have a useful property in that consecutive numbers differ in only a single bit position. The 3bit gray code is given below.

0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
Design a 3bit modulo 8 Gray code counter FSM that has no inputs but produces three outputs. When reset the output should be 000. On each clock edge the output should advance to the next Gray code. After reaching 100, it should repeat with 000. Implement the circuit using combinational logic and Dflip flops.
Problem 18:
Design an FSM that detects a stream of two consecutive 1’s in a stream of 0’s and 1’s. Implement it using a combination of sequential and combinational logic.
INPUT:0110111010….
OUTPUT:0010011000….