NAND Gate Logic
NOT-AND gate. Universal gate - can build any logic circuit. Output false only if all inputs true.
Visualization
Interactive visualization for NAND Gate Logic
Output: 1
NAND Gate:
- • NOT AND - output 0 only if both inputs 1
- • Universal gate
Interactive visualization with step-by-step execution
Implementation
1function nandGate(a: boolean, b: boolean): boolean {
2 return !(a && b);
3}
4
5function nandGateMultiple(...inputs: boolean[]): boolean {
6 return !inputs.every(x => x);
7}Deep Dive
Theoretical Foundation
Boolean NAND: ¬(A ∧ B). Truth table: 1∧1=0, all else 1. Universal: can build AND, OR, NOT from NAND. Widely used in IC design.
Complexity
Time
O(1)
O(1)
O(1)
Space
O(1)
Applications
Industry Use
CMOS integrated circuit design
Memory cell implementations (SRAM)
Microprocessor logic units
FPGA and ASIC standard cell libraries
Digital signal processing circuits
Universal logic implementations
Use Cases
Related Algorithms
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LCM (Least Common Multiple)
Calculate the Least Common Multiple (LCM) of two integers - the smallest positive integer that is divisible by both numbers. The LCM is intimately related to the GCD through the formula: LCM(a,b) = |a×b| / GCD(a,b). This relationship allows us to compute LCM efficiently using the Euclidean algorithm for GCD, achieving O(log min(a,b)) time complexity instead of naive factorization methods.
Sieve of Eratosthenes
Ancient and highly efficient algorithm to find all prime numbers up to a given limit n. Invented by Greek mathematician Eratosthenes of Cyrene (276-194 BC), this sieve method systematically eliminates multiples of primes, leaving only primes in the array. With O(n log log n) time complexity, it remains one of the most practical algorithms for generating large lists of primes, vastly superior to trial division which runs in O(n² / log n) time.
Prime Factorization
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