# Questions tagged [digital-circuits]

Digital circuits use logic gates as the basic building block. A logic gate performs a logical operation on binary inputs and produces a single binary output. The Primary Logical operations are AND (conjunction), OR (disjunction) and NOT (negation).

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### General Approach To Calculate Minimum Number Of Flip-Flops Required

In the previous two years of the GATE exams, a question has been asked for finding number of flip flop's for counting sequence $0−1−0−2−0−3$ in 2016 and $0−0−1−1−2−2−3−3−0−0$ in 2015. But still, the ...
187 views

### How do you compute and compare the delays between a (4:2) compressor and (3,2) counter carry save tree?

My question: How is Table 6.8 shown below computed for different operands? For example, for 3 operands how did they compute: Number of levels using (3,2) = 1 Number of levels using (4;2) = 1 ...
2k views

### Do Karnaugh maps yield the simplest solution possible?

I'm learning to use a Karnaugh map, but I'm not sure if I obtained the simplest expression possible. Have a look at this example: Truth table (inputs are A B C; output is F): ...
1 vote
59 views

### Prove or disprove that the Quine-McCluskey method generates the circuit with the minimum inputs and minimum gates?

Recently, when I self-learnt Discrete Mathematics and Its Applications 8th by Kenneth Rosen, it says in 12.4 Minimization of Circuits which uses the Karnaugh Map or the Quine-McCluskey method: ...
75 views

### Make the forward counter go down

Suppose, I have a 4-bit binary Incrementor that uses XOR gates to increment the inputted number by the value of 1 (b0001, to be precise). Suppose, we connect it to 4 D-Flip-Flops (DFF) to create a ...
59 views

### Is there an algorithm to implement N-input-gates using smaller gates?

To borrow part of a description from a similar but distinct question: there exist 2^(2^N) different functions which accept N binary inputs and return a 1 bit output. For the purposes of my question I ...
1 vote
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### How can I connect a drive to a 16 bit custom intel 8088 system?

I'm embarking on a long-term project, aiming to build a computer based on the Intel 8088 architecture. This venture provides an excellent opportunity to deepen my understanding of computer hardware ...
1 vote
120 views

### $n \pmod k$ circuit

I wondered if, for a fixed integer $k ≥ 3$, how can I construct a circuit for each $n \in \mathbb{N}$, that takes as input an n-bit integer $x$ and outputs whether 3 divides $k$? Considering an n-bit ...
19 views

### What are some good books for vlsi cmos design? Or some good educational software?

I'm a student trying to learn more about CMOS design, I already understand assembly and computer architecture, but VLSI is very interesting and I was wondering if you guys knew some good books/games ...
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### Why is 2's complement used for representing negative numbers?

So I was reading the use complement operation in the digital logic and found, it is used to give additive inverse of the number and subtracting a number (like we do) is difficult for computer. So it ...
8k views

### Connection between NAND gates and Turing completeness

I know that NAND gates can be used to create circuits that implement every truth table, and modern computers are built up of NAND gates. What is the theoretical link between NAND gates and Turing ...
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### Ideal less-than-or-equal circuit for multiple inputs?

I'm interested in what the best way is to design a circuit that takes multiple values as input, and then outputs which value is the lowest. If multiple values are the lowest, it outputs "true&...
19 views

### Logical circuit for priority resolution in interrupt controllers (with configurable priority, not fixed)

I'm interested in what the typical solution is for priority resolution in interrupt controllers. I assume a hardware logic circuit is used, and not software. For interrupt controllers with fixed ...
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### The definitions of terms in $P=CV^2f$

My textbook gives the equation for the power dissipation $$P=CV^2 f$$ but after reading it a couple times, I can't get very clear on exactly what each of these is measuring. It describes $P$ as the ...
34 views

### SOP Boolean expression of state variable and output of a Moore FSM

Disclaimer: I'm studying for an exam, but I don't have to hand in anything. I have the state transition diagram of the FSM and its states encoding: I want to find the sum-of-products (SOP) Boolean ...
1 vote
196 views

### How do you write a logic function to determine if one 2s complement binary number is less than another?

Working on logic design in class, and I'm trying to figure out how to write a specific logic function [and by write, I mean something along the lines of (x NOR y) OR (a NOR b), for example] It asks to ...
1 vote
34 views

### Did Jon von Neumann know about Claude Shannon's work when he wrote the "First Draft of a Report on the EDVAC?"

In the "First Draft" JvN described an adder circuit to do binary addition, which was a much faster way of doing computer addition than using decimal lookup tables as the ENIAC had done. JvN'...
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### is duality principle in boolean algebra is true for every expression

Let say A = 1 and B = 1 and then A+B = 1 now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0 but this is not 0, because 1.1 = 1, so please anyone clear my ...
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### K-Maps (Digital Logic, Computer System Architecture)

While i was going thru my course in Computer System Architecture (book taken Morris Mano) , I saw a question on KMaps can be solved in either of the ways but couldn't get which one to use when :- I’m ...
1 vote
276 views

### Combinational logic check if bits is prime

I wonder if there's Digital Logic Circuit (using combinatorial logic gates) that check if number is prime or not. For example given input fixed 8-bit that will produce 1-bit output. 00000101 will ...
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### Need to define output functions from logic circuit

i was given a this circuit as exam question So we need to define functions g and f. I defined them as $g(x,y,z) = x \oplus y \oplus z$ and $f(x,y,z) = (x \oplus y) \cdot z$. By definition known that ...
4k views

### Addition of 3 bits using Full Adder when the initial carry bit is 0

How do I add 3 bits using full adder and basic gates, when the initial carry bit is 0?? I have tried using two full adders where two terminals of the first adder gets the first two inputs then the ...
1 vote
183 views

### How are instructions from software sent to digital circuit in cpu?

I am studying computer architecture in my university and there is something that's troubling me. I get the bigger picture of how instructions are executed in the fetch - execute cycle and the complete ...
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### A query regarding Definition of Circuit Family and Languages

This is a query regarding the definition of Circuit Family and Language (in the same Context). The textbook definitions of each are: Language: A function whose inputs and outputs are a finite bit of ...
958 views

### Alu architecture of a Hack Computer

I'm currently studying the ALU architecture (of a Hack computer) and how it works. As part of my assignments, I have been asked the following question: If we want the ALU to compute the function y-1, ...
1 vote
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### How many functions require precisely $n^2$ gates?

I'm trying to determine an asymptotic bound on the cardinality of the following set of functions. It is the functions with $n$-bit inputs, $\{0,1\}$ output, and requires precisely $n^2$ NAND gates. I'...
1 vote
191 views

### What is combinational circuit?

I'm reading the Digital Design and Computer Architecture by David Harris, Sarah Harris. The authors give the following definition of combinational logic: A combinational circuit’s outputs depend only ...
1 vote
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### How do I compute the power consumption of a DRAM refresh?

Given a DRAM-based memory system with a total capacity of $x$ bytes, $y$ DRAM rows and a refresh time of $t$ milliseconds, how do I compute the power consumption for one DRAM refresh? I couldn't find ...
1 vote
102 views

### What is the intuitive logic behind the working of the Variable Entered K-Map (VEM)?

In this site here they have just said how to minimize a function using VEM. But no intuitive logic behind the same has been stated, making it too mechanical. And I am very bad at memorizing things, so ...
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I'm learning about logic circuits and I've come across full adder. In the book they derived its two carry out expressions - Cout = x&&y || x&&z || y&&z and Cout = x&&...
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### How to calculate the output frequency of this counter?

The present state Q2,Q1,Q0 of the counter before applying the clock pulse was (101). If the input Clock frequency to the circuit is 100KHz, then the output frequency of the circuit will be ? My ...
548 views

### Karnaugh Map: does maximal overlap always produce simplest boolean expression?

Suppose I have a 4x4 Karnaugh map with a few cells that are don't cares, and there are two ways of producing 3 groups of 4 cells. One of these ways overlaps groupings more that the other. Is one way ...
180 views

### Proof of universality in the circuit model

I'm starting to study Turing machines, the Church-Turing conjecture and the circuit model. In particular, I'm interested in the proofs of universality that one can find in this context. So far, I have ...
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### Building an ALU on nandgame's website

I'm working on nandgame's website found here. I'm working on the ALU and here is an image of my implementation: My Implementation: And I compared it to this website's solution: Solution However when ...
1 vote
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### What can this circuit be useful for?

I have calculated the boolean functions for $r$ and $f$: $f = \overline{s_1} \cdot s_0 + s_1 \cdot \overline{s_0}$. $r = \overline{s_0 \cdot s_1 \cdot s_2 \cdot s_3}$. Do you have an idea what an ...