Computer Science: An Overview (13th Edition) (What's New in Computer Science)
13th Edition
ISBN: 9780134875460
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Textbook Question
Chapter 1.1, Problem 4QE
- a. If the output of an AND gate is passed through a NOT gate, the combination computes the Boolean operation called NAND, which has an output of 0 only when both its inputs are 1. The symbol for a NAND gate is the same as an AND gate except that it has a circle at its output. The following is a circuit containing a NAND gate. What Boolean operation does the circuit compute?
- b. If the output of an OR gate is passed through a NOT gate, the combination computes the Boolean operation called NOR that has an output of 1 only when both its inputs are 0. The symbol for a NOR gate is the same as an OR gate except that it has a circle at its output. The following is a circuit containing an AND gate and two NOR gates. What Boolean operation does the circuit compute?
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We consider a circuit having four inputs and one output. The output has the value 1 if at least half of the inputs have the value 1. In this case, the circuit is a not-a-minority circuit.
1) Build a truth table for the circuit presented in the description above.
2) Using this truth table, find a Boolean expression which represents the same function, and by using Boolean algebra, simplify it as much as possible.
3) Verify the design of the circuit.
Task 4: Simplifying Boolean functions
Simplify the following Boolean expression
F (A, B, C) = (A+C") +C (C.A' + (B.A) +C
Draw the simplified Boolean expression using EWB. Find out the truth table of the circuit.
The NAND logic gate is universal, meaning that using gate alone,
we can implement any of the other logic gates. Find a way to define
NOT, AND, and OR, using only NAND gates and the input variables
I and y.
(a) NOT(2) =
(b) AND(x, y) =
(c) OR(x, y) =
Chapter 1 Solutions
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Ch. 1.1 - What input bit patterns will cause the following...Ch. 1.1 - In the text, we claimed that placing a 1 on the...Ch. 1.1 - Assuming that both inputs to the flip-flop in...Ch. 1.1 - a. If the output of an AND gate is passed through...Ch. 1.1 - Prob. 5QECh. 1.1 - Prob. 6QECh. 1.2 - If the memory cell whose address is 5 contains the...Ch. 1.2 - Prob. 2QECh. 1.2 - Design a sequence of steps that correctly...Ch. 1.2 - How many bits would be in the memory of a computer...
Ch. 1.3 - Prob. 1QECh. 1.3 - Prob. 2QECh. 1.3 - Prob. 3QECh. 1.3 - Prob. 4QECh. 1.3 - Prob. 5QECh. 1.3 - Prob. 6QECh. 1.4 - Here is a message encoded in ASCII using 8 bits...Ch. 1.4 - In the ASCII code, what is the relationship...Ch. 1.4 - Prob. 3QECh. 1.4 - Prob. 4QECh. 1.4 - Convert each of the following binary...Ch. 1.4 - Prob. 6QECh. 1.4 - What is the largest numeric value that could be...Ch. 1.4 - An alternative to hexadecimal notation for...Ch. 1.4 - What is an advantage of representing images via...Ch. 1.4 - Prob. 10QECh. 1.5 - Convert each of the following binary...Ch. 1.5 - Convert each of the following base ten...Ch. 1.5 - Convert each of the following binary...Ch. 1.5 - Express the following values in binary notation:...Ch. 1.5 - Perform the following additions in binary...Ch. 1.6 - Convert each of the following twos complement...Ch. 1.6 - Prob. 2QECh. 1.6 - Suppose the following bit patterns represent...Ch. 1.6 - Suppose a machine stores numbers in twos...Ch. 1.6 - In the following problems, each bit pattern...Ch. 1.6 - Prob. 6QECh. 1.6 - Prob. 7QECh. 1.6 - Prob. 8QECh. 1.6 - Prob. 9QECh. 1.6 - Prob. 10QECh. 1.6 - Prob. 11QECh. 1.7 - Prob. 1QECh. 1.7 - Prob. 3QECh. 1.7 - Prob. 4QECh. 1.8 - What makes Python an interpreted programming...Ch. 1.8 - Write Python statements that print the following:...Ch. 1.8 - Write Python statements to make the following...Ch. 1.8 - Write a Python statement that given an existing...Ch. 1.9 - Prob. 1QECh. 1.9 - Prob. 2QECh. 1.9 - Prob. 3QECh. 1.9 - Prob. 4QECh. 1.9 - Prob. 5QECh. 1.9 - Prob. 6QECh. 1.9 - Prob. 7QECh. 1.10 - Prob. 1QECh. 1.10 - Could errors have occurred in a byte from Question...Ch. 1.10 - Prob. 3QECh. 1.10 - Prob. 4QECh. 1.10 - Prob. 5QECh. 1.10 - Prob. 6QECh. 1 - Determine the output of each of the following...Ch. 1 - a. What Boolean operation does the circuit...Ch. 1 - a. If we were to purchase a flip-flop circuit from...Ch. 1 - Assume that both of the inputs in the following...Ch. 1 - The following table represents the addresses and...Ch. 1 - How many cells can be in a computers main memory...Ch. 1 - Prob. 7CRPCh. 1 - Prob. 8CRPCh. 1 - Prob. 9CRPCh. 1 - Prob. 10CRPCh. 1 - Suppose a picture is represented on a display...Ch. 1 - Prob. 12CRPCh. 1 - Prob. 13CRPCh. 1 - If each sector on a magnetic disk contains 1024...Ch. 1 - How many bytes of storage space would be required...Ch. 1 - Prob. 16CRPCh. 1 - Prob. 17CRPCh. 1 - Suppose a typist could type 60 words per minute...Ch. 1 - Prob. 19CRPCh. 1 - Prob. 20CRPCh. 1 - Prob. 21CRPCh. 1 - Prob. 22CRPCh. 1 - Prob. 23CRPCh. 1 - Prob. 24CRPCh. 1 - Prob. 25CRPCh. 1 - Prob. 26CRPCh. 1 - Prob. 27CRPCh. 1 - Prob. 28CRPCh. 1 - Prob. 29CRPCh. 1 - Prob. 30CRPCh. 1 - Prob. 31CRPCh. 1 - Prob. 32CRPCh. 1 - Prob. 33CRPCh. 1 - Prob. 34CRPCh. 1 - Prob. 35CRPCh. 1 - Prob. 36CRPCh. 1 - Prob. 37CRPCh. 1 - Prob. 38CRPCh. 1 - Prob. 39CRPCh. 1 - Prob. 40CRPCh. 1 - Prob. 41CRPCh. 1 - Prob. 42CRPCh. 1 - Prob. 43CRPCh. 1 - Prob. 44CRPCh. 1 - Prob. 45CRPCh. 1 - What would be the hexadecimal representation of...Ch. 1 - Prob. 47CRPCh. 1 - Prob. 48CRPCh. 1 - Prob. 49CRPCh. 1 - Prob. 50CRPCh. 1 - Prob. 51CRPCh. 1 - Prob. 52CRPCh. 1 - Prob. 53CRPCh. 1 - Prob. 54CRPCh. 1 - Prob. 55CRPCh. 1 - Prob. 56CRPCh. 1 - Prob. 57CRPCh. 1 - Prob. 58CRPCh. 1 - Write and test a Python script that, given a...Ch. 1 - Prob. 61CRPCh. 1 - Prob. 2SICh. 1 - Prob. 3SICh. 1 - Prob. 4SICh. 1 - Prob. 5SICh. 1 - Prob. 6SICh. 1 - Prob. 7SI
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- Question 2: A combinational circuit has 4 inputs (A, B, C, D) and 1 output (F). ABCD represent a majority function. The output of the majority function is equal to 1 if the input variables have more 1's than O's, otherwise the output is 0. a. Construct the truth table of the required circuit. b. Implement the minimized expression of F using 3-level all NAND gate circuit. Implement a 2-1Multiplexer using three-state buffers.arrow_forwardDesign a circuit that implements function p below using AND, OR, and NOT gates. DO NOT change the form of the equation.arrow_forwardQ1. Design a logic circuit that perform. the gray code on the 4-input binary weighted code 2421 using Karnugh Map (K.M) implementation method? Using Electronic Workbench. i.e. weighted code 2421 Gray codearrow_forward
- Build a circuit ending AND, OR and NOT gates to implement the following truth table…arrow_forward➤ Consider the following Boolean expression F = AB + CD. ✓ Draw the logic diagram of the function F. ✓ Redraw the logic diagram using an equivalent NAND gate.arrow_forwardla. Draw the truth table for the following set of gates with inputs A, B, C and D and result R: NOT - A OR AND - B R OR NOT -C - -D - b. Use the truth table to generate a Booleanexpression describing the function (using minterms))arrow_forward
- The following logic circuit has four inputs A, B, C, and D. Write the Boolean expression for X. Can we simplify it?arrow_forwardGiven the expression F(X,Y,Z)= XY + Z, draw the circuit using NOT and OR gates only. How many NOT and OR gates will be needed? O 3 NOT and 1 OR O 2 NOT and 2 OR O 2 NOT and 1 OR 1 NOT and 3 OR O 1 NOT and 2 ORarrow_forwardDesign a three-input combinational logic circuit for F(A,B,C)= )7,6,4,2,0(m. Simplify the output expression of F. You may choose to use either Boolean algebraor Karnaugh map techniques to simplify the design. Finally, implement the design circuit from the final output expression of Fusing only AND, OR and NOT logic gates.arrow_forward
- Gate Universality We know that the NAND gate is universal, so all other gates can be built using just NAND gates. We also mentioned that the NOR gate is universal, and can serve the same purpose. In this question we will look at NOR gates. Draw the AND operation as a circuit using a minimal number of NOR gates. Check your design in (a) by showing the full truth table for it. Draw the OR operation as a circuit using a minimal number of NOR gates. Check your design in (c) by showing the full truth table for it. Draw the NOT operation as a circuit using a minimal number of NOR gates. Check your design in (e) by showing the full truth table for it.arrow_forward2. Write the Boolean expression of the given logic circuit as shown below. X. F =arrow_forward1. A possible logic circuit design for a 3-bit even parity bit generator is shown below. Analyze the circuit and trace its outputs given different input combinations. Complete the circuit's truth table. Also generate its Boolean expression. Inputs Output C A B 1 1 1 1 1 1 1 1 Boolean expression: Considering your derived Boolean function, simplify the equation using Boolean algebra. P.arrow_forward
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