Logic Gates

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Show your work for each problem.

1.
Which gate gives output 1 only when both inputs are 1?
1. a)OR
2. b)XOR
3. c)NOR
4. d)AND
2.
An OR gate has the inputs $A = 0$ and $B = 1$ . What is the output? (Write 1 or 0.)
3.
A NOR gate has the inputs $A = 0$ and $B = 0$ . What is the output? (Write 1 or 0.)
4.
For the inputs $00$ , $01$ , $10$ , $11$ a gate gives the outputs $0, 1, 1, 0$ . Which gate is it?
1. a)XOR
2. b)NAND
3. c)AND
4. d)OR
5.
The inputs are $A = 1$ and $B = 1$ . Find the output of an AND, an OR and an XOR gate.
6.
$A$ goes through a NOT gate, and its output and $B$ go into an OR gate: $Y = \neg A \lor B$ . Find $Y$ for $A = 1$ , $B = 0$ .
7.
$A$ and $B$ go into an OR gate, and its output goes through a NOT gate. Which expression describes the circuit?
1. a) $\neg A \land B$
2. b) $\neg(A \lor B)$
3. c) $\neg A \lor \neg B$
4. d) $\neg(A \land B)$
8.
In how many of the 4 input rows does a NAND gate give the output 1?
9.
$A$ and $B$ go into an AND gate. $B$ and $C$ go into an OR gate. Both outputs go into an XOR gate, which gives $Y$ . Find $Y$ for $A = 1$ , $B = 0$ , $C = 1$ .
10.
A circuit computes $Y = (A \land B) \lor \neg C$ . Find $Y$ for $A = 0$ , $B = 1$ , $C = 1$ .
11.
In gate notation ( $\cdot$ = AND, $+$ = OR, bar = NOT), find $Y = \overline{A \cdot B} + C$ for $A = 1$ , $B = 1$ , $C = 0$ .
12.
Which inputs make a NOR gate give the output 1?
1. a)A = 1, B = 1
2. b)A = 1, B = 0
3. c)A = 0, B = 0
4. d)A = 0, B = 1
13.
A half adder gets $A = 0$ and $B = 1$ . It outputs the sum digit $S = A \oplus B$ and the carry digit $C = A \land B$ . Find $S$ , $C$ and the value of the binary number $CS$ .
14.
A circuit computes $Y = (A \oplus B) \land \neg C$ . In how many of the 8 input combinations is $Y = 1$ ?
15.
Both inputs of a NAND gate are connected to the same signal $A$ . Find the output for $A = 0$ and for $A = 1$ , and decide how many NAND gates you need to build one AND gate.
16.
Which circuit gives the same output as an XOR gate for all inputs?
1. a) $(A \lor B) \land \neg(A \land B)$
2. b) $(A \land B) \lor \neg(A \lor B)$
3. c) $\neg A \land \neg B$
4. d) $(A \lor B) \land (A \land B)$
17.
Three judges press a button (1) or not (0). A light shows $Y = (A \land B) \lor (A \land C) \lor (B \land C)$ . Find $Y$ for $A = 1$ , $B = 0$ , $C = 1$ , then count the input combinations with $Y = 1$ .
18.
A circuit computes $Y = \overline{A + B} + A \cdot B$ (bar = NOT, $+$ = OR, $\cdot$ = AND). In how many of the 4 input rows is $Y = 1$ ?