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
479 questions
2 votes
3 answers
430 views
Karnaugh map transforming expression into a k map
I'm not sure if I can post this here, but I need help understanding how to transform an expression like this A'C(A'BD)' + A'BC'D'+ AB'C into a K -map
-3 votes
1 answer
144 views
How to achieve NOR gate and NAND gate?
I need to achieve NOR gate using only NAND gates, and achieve NAND gate using only NOR gates. I have tried using De Morgan's law, which states that (AB)'=A'+B' and <...
2 votes
1 answer
101 views
Can I optionally override a three-way selector with two two-way switches?
I have a selector switch with four wires: one common (C) and three position wires (P1, P2, P3). Normally, the output follows the selector so that C is connected to whichever P is active. I want to ...
7 votes
1 answer
1k views
Why does one implementation of an XOR gate with only NAND gates need 4 whereas the one I sketched up has 5?
When deriving the XOR implementation with only NAND gates, I attempted to make versions of the AND OR and NOT gates used in it with NAND gates and then put it together and start pulling out ...
-2 votes
2 answers
133 views
How to minimize CMOS transistor count for the following Boolean Expression: Y = !(C + A*B)
I know that the expression itself can easily be implemented with an AND and a NOR gate. X = A AND B Y = C NOR X My CMOS gate ...
2 votes
3 answers
547 views
implement multiple XOR with the minimum number of NAND gates
I need to implement the following function en1 = (b4⊕b3⊕b2⊕b1⊕b0)' using the minimum number of NAND gates. simulate this circuit – Schematic created using ...
1 vote
2 answers
127 views
How is this flip flop expressed algebraically?
How is the following picture expressed in logical symbols? I’m confused about the crossing wires on the outputs to inputs. Ref:ref
1 vote
1 answer
85 views
Implementing a boolean function using at most 10 gates
I was given the following question: Given the following truth table, implement the 2 functions needed for \$cout\$ and sum (\$s\$) using only XNOR, NAND and OR (only the 2 inputs version for each gate)...
0 votes
0 answers
54 views
How do I go about kmapping a boolean expression of 6 variables using splitting?
Say I want the SOP. I plan to split the kmap into kmaps of 3 variables each then get their respective SOPs. After which, do I need to combine the SOPs? If so, how? What if my SOPs from all kmaps are (...
2 votes
2 answers
164 views
How do I reduce \$\bar{A}\bar{B}\bar{C} + \bar{A}\bar{B}C + A\bar{B}\bar{C} + A\bar{B}C\$ to \$\bar{B}\$?
Can someone explain how the simplified version of this boolean expression is B'? I got A'B' + AB'.
0 votes
1 answer
159 views
How Do I Simplify These Massive Boolean Equations?
I'm fairly new to this, and I am working on a computer that would play tic-tac-toe with you. It takes the position convert it into binary split it into different inputs, run it through some function ...
0 votes
1 answer
193 views
Trying to minimize product terms for GAL16V8
I am building an accessory for a 6502-based computer, and am trying to stick with (reasonably) period-era components. To this end I am using a GAL16v8 (specifically an ATF16V8C) to handle register ...
0 votes
1 answer
62 views
Is this Boolean Expression in Standard POS form or not
I am trying to find if the expression X.(W'+YZ) is POS form or not. My thinking: ...
0 votes
1 answer
115 views
How to approach the highlighted part of the question?
The boolean expression for Z for the four input module came out to be A0A1A2+A0A2A3+A0A1A3+A1A2A3 I am attaching my work here.
0 votes
1 answer
109 views
Boolean Algebra Confusion
So Im going through the nand2tetris course on my own for fun, and I am at the half adder/adder portion. The half adder was pretty easy just based on the truth table, but the full adder im having more ...