Some Questions and Answers After Class Gates and Circuits

1. Give the three representations of an AND gate and say in your words what AND means.

The mean is that the gate will output 1 only when two input signals are both 1.

2.Give the three representations of an XOR gate and say in your words what XOR means.

The mean is that the gate will output 1 only when two input signals are different.(if one is 0,the others must be 1)

3.Draw a circuit diagram corresponding to the following Boolean expression: (A + B)(B + C)

4.Show the behavior of the following circuit with a truth table:

A B X 0 0 1 0 1 1 1 0 0 1 1 1

5.What is circuit equivalence? Use truth table to prove the following formula.

(AB)′=A′+B′

The same output for each corresponding inputvalue combination for two circuits.

A B (AB) (AB)′ 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 A B A′ B′ A′+B′ 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0

6.There are eight 1bit full adder integrated circuits. Combine them to 8bit adder circuit using the following box diagram.

To add two eight-bit values, we can duplicate a full-adder circuit eight times. The carry-out from one place value is used as the carry-in to the next highest place value. The value of the carry-in for the rightmost bit position is assumed to be zero, and the carry-out of the leftmost bit position is discarded (potentially creating an overflow error).

7.Logical binary operations can be used to modify bit pattern. Such as

(X8X7X6X5X4X3X2X1)2 and (00001111)2=(0000X4X3X2X1)2

(X8X7X6X5X4X3X2X1)2 and (00001111)2=(0000X4X3X2X1)2

We called that (00001111)2 is a mask which only makes low 4 bits to work. Fill the follow expression:

I:(X8X7X6X5X4X3X2X1)2 or (00001111)2 = (X8X7X6X51111)2

II:(X8X7X6X5X4X3X2X1)2 xor (00001111)2 = (if the digit of follow is different from the digit of behind ,the connecting digit in the answer is 1,else,the connecting digit in the answer is 0.)

III:((X8X7X6X5X4X3X2X1)2 and (11110000)2) or (not (X8X7X6X5X4X3X2X1)2 and (00001111)2)= (X8X7X6X5NX4NX3NX2NX1 )2

(NX1 is the same as X1′)