# 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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### 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 ...
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### Decoder inputs and outputs given in brackets. What does it mean?

I am given that the inputs and the output of a decoder are B(1:0) and R(3:0) respectively. What should be R if B is 01₂? I don't understand what format the input and outputs are given in. Can someone ...
1 vote
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### 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 ...
1 vote
24 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 ...
176 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
36 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'...
39 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 ...
28 views

### Number of possible boolean functions in a DAG of lookup tables?

A K-input lookup table (K-LUT) can represent any function with K boolean inputs and a single boolean output. The number of possible functions represented by this LUT is $2^{2^K}$ according to this ...
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### Mechanism of Howard's algorithm

How does Howard's algorithm avoids re-mapping of the non-critical nodes ?
1 vote
102 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
105 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
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### 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 ...
70 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 ...
145 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 ...
154 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 ...
226 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 ...
1k 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 ...
1 vote
62 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 ...
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### 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 ...
63 views

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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### 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 ...
1 vote
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### 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 ...
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### 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
245 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 ...
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 ...