Assignment:
Q1. Gates
Implement the 1 bit full adder using only:
1. 2 input NAND gates
2. 2 input NOR gates.
Q2. Boolean Functions
Using the laws of Boolean algebra, minimize the number of operators in the following Boolean functions:
1. wy'+ wx'y + wxyz + wxz'
2. abc + a'd + b'd + cd
Q3. Given the following truth table, write the Boolean function, simplified as much as possible. Draw the logic circuit using only 2-input AND, OR and NOT gates.
xwyz F
|
0000
|
0
|
|
0001
|
1
|
|
0010
|
0
|
|
0011
|
0
|
|
0100
|
0
|
|
0101
|
1
|
|
0110
|
0
|
|
0111
|
1
|
|
1000
|
0
|
|
1001
|
1
|
|
1010
|
1
|
|
1011
|
1
|
|
1100
|
0
|
|
1101
|
1
|
|
1110
|
1
|
|
1111
|
1
|
Q4. Logic Operations
Given A,B are 32 bits wide. Write the result stored in B after each one of this operations (for each line, assume B has the value assigned to it by the previous operation). Write your results using hexadecimal numbers. A = 0x12345678 (initial value)
1. B = A AND 0x87654321
2. B = B XOR 0x33333333
3. B=BORA
4. B=NOTB
5. Combinational Circuits
Design a binary-to-decimal decoder whose inputs are 4-bit BCD-encoded numbers (x3x2x1x0) and whose outputs are lines (d9, d8,. . . , d0). The circuit should be minimized as much as possible.
Provide complete and step by step solution for the question and show calculations and use formulas.