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).

Filter by
Sorted by
Tagged with
3 votes
1 answer
2k views

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 ...
2 votes
2 answers
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 ...
4 votes
2 answers
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
0 answers
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: ...
0 votes
1 answer
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 ...
0 votes
3 answers
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
0 answers
20 views

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
3 answers
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 ...
0 votes
0 answers
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 ...
0 votes
2 answers
167 views

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 ...
19 votes
4 answers
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 ...
0 votes
0 answers
41 views

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&...
0 votes
0 answers
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 ...
0 votes
0 answers
47 views

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 ...
0 votes
0 answers
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
3 answers
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
0 answers
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'...
0 votes
2 answers
92 views

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 ...
0 votes
1 answer
37 views

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
2 answers
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 ...
0 votes
0 answers
52 views

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 ...
0 votes
2 answers
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
2 answers
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 ...
2 votes
1 answer
70 views

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 ...
0 votes
0 answers
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
1 answer
44 views

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
1 answer
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
1 answer
145 views

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
0 answers
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 ...
0 votes
1 answer
71 views

Full adder carry expression

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&&...
-1 votes
1 answer
2k views

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 ...
0 votes
0 answers
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 ...
2 votes
1 answer
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 ...
0 votes
0 answers
1k views

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
1 answer
64 views

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 ...
-1 votes
2 answers
61 views

Minimize circuit functions

$\begin{array}{rrrr | rr } 0& 0 & 0 & 0 & 1 &1 &1 &1 &1 & 1&0 \\ 0& 0 & 0 & 1 & 0 &1 &1 &0 &0 & 0&0 \\ 0& 0 & 1 &...
2 votes
0 answers
97 views

How does the structure of a Luk-Vuillemin multiplier differ from a Wallace or Dadda multiplier?

I've read that Luk-Vuillemin multipliers are similar to Wallace multipliers but partition their inputs in a different way. How exactly does this partitioning work, how does it change the structure of ...
0 votes
1 answer
29 views

Is this truth table possbile

I am trying to figure out if this truth table is possible. I've tried inverting the numbers, adding them, subtracting them, but I still cant find anything that works. I am starting to think that this ...
0 votes
2 answers
894 views

SIMD Utilization

Can anyone help me understanding this exercise? We define the SIMD utilization of a program run on a GPU as the fraction of SIMD lanes that are kept busy with active threads during the run of a ...
0 votes
0 answers
33 views

Which gates are “pre computation” universal?

In the following, by “functions” I will mean 2 input 1 output Boolean logic functions (for conciseness). A function is called “universal” if by using it (sometimes multiple times, chained together), ...
1 vote
1 answer
795 views

Minimizing a multiple output circuit with K-maps - and without

I'm currently working on learning to minimize a circuit which has multiple outputs using K-maps. My universities script seems rather unhelpful to me which left me in a spot where I have a very rough ...
0 votes
2 answers
4k views

Minimum number of bits to represent negative number

Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form? My attempt: 32 = 0100000 ( 1st zero - sign bit as positive) So to represent +32 we ...
0 votes
1 answer
672 views

Hamming code distance and error detection

Suppose that data are transmitted in blocks of sizes 1000 bits. What is the maximum error rate under which error detection and retransmission mechanism (1 parity bit per block) is better than using ...
2 votes
2 answers
822 views

Prime Implicants in Boolean Function

A Boolean function $F(X_1, X_2, X_3, X_4, X_5, X_6)$ of six variables is defined as $F = 1$, when three or more input variables are at logic 1. otherwise 0. How many essential prime implicants does F ...
4 votes
1 answer
1k views

Analog circuits for neural networks?

Neural networks in machine learning are inherently a continuous model of computation. Yet we use digital logic circuits with floating point numbers to "emulate" this continuity. I am wondering: is ...
3 votes
1 answer
61 views

Efficient method for generating the smoothing function

The smoothing function of a boolean function with respect to one of its variables is the disjunction of its cofactors. For example given a Boolean function F(a,b,c) the cofactors with respect to a are ...
1 vote
0 answers
93 views

Minimum no. of flip flops for the given sequence

We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of flip-flops required to implement this counter is________ According to me, the ...
-3 votes
2 answers
641 views

D - Latch or D Flip Flop?

I have a diagram (https://i.stack.imgur.com/UK16E.jpg) where it is either a D Latch or D Flip Flop. I am trying to figure out which one it is and why. If it is a D Flip Flip, I also need to know which ...
0 votes
1 answer
580 views

Simplifying SOP: implementing OR with NAND

I am learning how to implement basic logic gates using NAND. I have learnt that you can use De Morgan's theorem as such: $a+b = \bar{\bar a} + \bar{\bar b} = \overline{(\bar a *\bar b)}$ In other ...
0 votes
0 answers
32 views

Register output glitches and memory writes

When changing the write enable signal, of a memory element, from 1 to 0, what effect does the pipeline's register's output glitch have? Glitch that all of digital logic has, for the time of ...