# Questions tagged [boolean-algebra]

In mathematics and mathematical logic, boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra is used in the analysis and simplification of digital (logic) circuits

459 questions
Filter by
Sorted by
Tagged with
30 views

### Help needed Creating a truth table and a logic circuit using a statement given [closed]

i have gotten this question in my assignment, i'm quite confused about this and don't know where and how to start doing it, any help is appreciated
• 1
1 vote
54 views

### Which is the preferred circuit layout? Horizontal vs. Vertical (Combinational logic)

I have 2 equivalent circuits Picture 1 (Compact, a bit messier) Picture 2 (Easier to read, less compact)
66 views

### Building a circuit which adds 2 signed numbers

I am developing circuitry to add 2 numbers with sign.They have the form: $$b_{1}:(sign)|(absoluteval)$$ I realised that the calculation of the sign of the addition of such 2 binary numbers must be ...
59 views

### Converting this boolean expression to NOR only expression

I was given an expression which I simplified using k-maps to obtain the following: ~WY + W~YZ + ~W~X~Z I followed along with some of the other workings people have done for converting functions, but ...
34 views

### Is it necessary to have all variables of a boolean expression in its POS or SOP form?

For example, if we have a boolean expression, anything like: X= A′ B + CD + (A+B)′ [ACD + (BE)′ ] We know this can be CD + A'. ...
79 views

### Full-subtractor boolean expression minimization

I'm looking at the standard full subtractor circuit and have been trying to understand how the circuit is derived/synthesized based on a web tutorial. I can follow the derivation of the truth table in ...
77 views

### Why does NOR need one more output to the multiplexor but NAND not in ALU?

Recently, I was learning "Computer Organization and Design: The Hardware/ Software Interface" riscv 2nd Edition by "David A. Patterson" In appendix A, A-37 shows the question in &...
• 83
138 views

### How should I proceed with implementing a multiple sequence detector FSM?

I was given the following question: Design a finite state machine (FSM), with not more than 4 states, that will detect more than one number of 1’s in the previous 3 samples. For example - ...
• 121
1 vote
108 views

### How can I improve my ladder logic diagram of a vending machine?

I am trying to create a coffee and tea machine using a ladder logic diagram. There are small, medium, and large sizes. This is where I am now: Can you give me any ideas or corrections on how to ...
740 views

### Electrical counterpart: Logical not

I'm building a circuit where I must receive a signal from a logical not. More specifically, I'm looking for a real-life electrical circuit element/component that provides power/signal on the output ...
• 45
388 views

### How can I convert boolean algebra to logic gates?

I have a very large boolean algebra equation that I designed in Logic Friday, but it got too complicated for it to turn into gates. Note that I am a programmer, not an electrical engineer, so please ...
1 vote
58 views

### Automatic MCU Reset for Battery-Powered Single-Button Product

I'm designing a battery-powered product with a USB-C PD charging port and a single user button. I'd like to be able to build in a feature for recovery and re-programming where the user holds down the ...
• 375
68 views

### How to express this logic circuit with output feedback as boolean expression?

Q1. How to express this circuit as boolean expression? It uses the output as input (feedback??) to part of the circuit. Is it a special type of circuit? Q2. How do I simplify it as Nand-only ...
• 101
1 vote
139 views

### How do we get a -1 in a 1-bit ALU?

In the 1-bit ALU and the table that is shown below, as you can see, the output is -1 when F0 = 1, F1 = 1, ENA = 0, ENB = 0, INVA = 1, INC = 0. The table is taken from a book (Structured Computer ...
• 133
31 views

### Logism: Further reducing number of logic gates in a circuit

I have this circuit attached below that has an arbitrary behavior. I want to reduce the number of gates more if possible. I've taken its expression and passed it through multiple boolean expression ...
132 views

### How do I simplify the two boolean expressions?

I have the two expressions that I have already simplified as much as possible: C̅D̅ ∨ A̅B̅D ∨ A̅BC̅ AB ∨ AC ∨ B̅C̅ However, I know that you can simplify both expressions even further per KV diagram: ...
93 views

### My logisim simulation of a sequential circuit using T Flip-Flop is stuck at 1-1-1

I have an assignment that required us to draw a logic diagram of this sequence using T-flipflops: The state diagram: I obtained this Boolean algebra expression using a KMAP: ...
1 vote
274 views

### Can the output of a logic gate be split to serve as input for other logic gates?

In the textbook picture, they use 5 NOT gates, repeatedly splitting the R input only to have it go into a different NOT gate. Are you allowed to put the input of R into a single NOT gate, and split ...
34 views

### Understanding OLD PEEL173 code

I have some code for a PEEL173 form the early 90's. I would like to understand the logic of this code, but I don't recognize this syntax. Question 1: Do you recognize the syntax of this language? What ...
79 views

### Similarity in "carry and sum" and "difference and borrow"

i know carry and sum from all the sources i studied in YT (particularly KNOWLEDGE GATE) except neso academy that teaches using difference and borrow in same place as carry and sum Sources:- Knowledge ...
1k views

### simplify Boolean function F(A, B, C, D) = ∑ m(0, 1, 3, 4, 5, 7,8,9 11, 13,14,15)

Hello just got stuck simplifying this boolean function using four variable K-Map. I have to simplify this boolean function in terms of sum of minterms. ...
173 views

### Logic gate: electricity, voltage and meaning [duplicate]

I am confused by this kind of diagram (simplest, NOT gate): ------1------___Gate Here___-------0-------- Because my book tends to talk about electricity. So if I ...
• 23
106 views

### Transition table from state truth table

Assuming a simple binary state variable allocation can be made and that any unused states can be treated as don’t cares. How would I Design a corresponding transition table for this system including ...
95 views

### Need help determining CMOS circuits with logic function Y [closed]

I am trying to determine which of the CMOS circuits in the question below have the logic function Y, but I am having trouble understanding how to do so. I have tried looking at the circuits and ...
60 views

### Is my simplified Boolean expression correct?

I'm trying to simplify the following Boolean expression: A'(B'C'D' + BC'D' + BCD) + A(BC'D + BC'D + BCD + BCD' + B'C'D) I've already made a few steps to simplify it, but I'm not sure if I'm on the ...
146 views

### When given the maxterm of function, we can find its minterm of the function, which is also the complement of the maxterm,

When given the maxterm of function, we can find the minterm of the function, which is also the complement of the maxterm. When do we use one (maxterm) instead of the others (minterm/its complement)? ...
53 views

### Duality Principle, but confused by the example

The dual of a Boolean expression can be obtained by interchanging sums and products; also interchanging 0 and 1. But the dual of xy̅ + 1 is (x' + y) · 0 ( I think) Or the dual is (x + y) · 0. Q: do ...
1 vote
100 views

### Need help understanding why I get the logic circuit wrong

Could someone care to explain why the logic circuit for this boolean expression doesn't look like this? When I select "build circuit," on Logisim, I get a different result:
1 vote
62 views

### Kmap and boolean equation for a function

F(A,B,C,D) = Σm(1, 2, 4, 6, 8, 10, 11, 13, 15) Here's my try of the kmap: Are my kmap and boolean equation correct for this function?
1 vote
341 views

### How to convert SoP to NOR?

I have a logical expression: F = AB + AC + CB I know its equivalent expression via NOR: R = (A ⊽ B) ⊽ (A ⊽ C) ⊽ (C ⊽ B) It is assumed that the desired expression in NOR is unknown. I know De Morgan's ...
• 33
66 views

### Minimizing a Boolean Expression

From a 3 variable K-map I get the following expression: BC + B!C! *!=not I know that a + a!b = a, so does this mean that BC + B!C! = B + C?
• 57
1 vote
284 views

### About DEMUX/demultiplexer: can any Boolean function be realized with the help of demultiplexers?

I know that as we OR the outputs of a DEMUX we can get a function as the first screenshot which states that an OR gate generates the one-set of the function. But can any Boolean function be realized ...
• 133
105 views

### Where am I wrong here? I don't know why I can't get it

Question: BOOLEAN SIMPLIFICATION: Prove that F(w,x,y,z) = w’x’y’z’+w’xy’z’+ wx’y’z’+wx’y’z+ wx’yz’+w’xy’z’+ w’x’yz is equals to F(w,x,y,z) = y’z’ + wx’ My solution: F(w,x,y,z) = w’x’y’z’+w’xy’z’+ wx’y’...
132 views

### Confusion in Duality Principle in Boolean Algebra

Maybe I have got some misconception while solving a problem. Lets a logic function, X=AB+A'C By applying duality principle, I can say that, X=(A+B)(A'+C) But I can't prove both are equal. I simplify ...
68 views

### Implying a boolean function by using 5 NANDS only - How to implant "1" using nand?

Function: f(a,b,c,d) = b' + c' + ad + a'd' I used Karnaugh map (4x4). Received that the function is all squares except square number 7 (there it is 0). Which means: Now what is the problem? When I do ...
1 vote
272 views

### For the 4x1 MUX shown below the Boolean Expression F(x,y,z) is [closed]

The output to a 4x1 MUX is : $Y=S_1'S_0'I_0+S_1'S_0I_1+S_1S_0'I_2+S_1S_0I_3$ My answer was : $F=A_{1}'A_{2}'x+A_{1}'A_{2}x+A_{1}A_{2}'y+A_{1}A_{2}y' \Rightarrow xyz'+xyz+y'z$ The correct answer is ...
324 views

### A three-input NAND gate is to be used as an inverter. Which one of the following measures will achieve better results?

The two inputs not used are kept open The two inputs not used are connected to ground (0 level) The two inputs not used are connected to logic supply (1 level) None of the above I get that we can ...
1 vote
86 views

### Show that specific functions are correct for a race-free Moore machine

Context: The goal here is to create a Latch that holds a state. We have two inputs x1, x2 and two outputs f1, f2. When (x1, x2) = (0, 1) or (x1, x2) = (1, 0) the outputs should be the same. When the ...
364 views

### Minimizing logic expression for two-input NAND gate implementation

I have recently been struggling with this homework problem that is requiring minimization of a logic expression to be implemented using all NAND gates. The problem requires a very small number of NAND ...
34 views

### Express state of overflow as function?

Making an ALU I want a signal that signals whenever an addition or subtraction changes the binary number from - to +. Each number u and v is 4-bits and therefore is marked by 0, 1, 2, 3 where 3 is the ...
211 views

### Why do we even need an OR gate? [duplicate]

Question This might be a naive question but hear me out, can't we just connect the two wires in parallel to build an OR gate? Like this: simulate this circuit – Schematic created using ...
• 133
1 vote