# Boolean Algebra : Gates, Truth Tables and Logic Operations

(See attached file for full problem description)

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For question #1, just use the example to show how to solve a problem like it is.

1. Gates Implement the 1 bit full adder using only:

1. 2 input NAND gates

2. 2 input NOR gates.

2. 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

3. 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

4. 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.

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