Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
NAND logic
open-in-new
<p>The <a href="/facts/Sheffer_stroke/rpXH07u4">NAND Boolean function</a> has the property of <a href="/facts/Functional_completeness/ncyHAsHH">functional completeness</a>. This means that any Boolean expression can be re-expressed by an <a href="/facts/Equivalence_relation/1MQ5rtkW">equivalent</a> expression utilizing only <a href="/facts/Sheffer_stroke/rpXH07u4">NAND</a> operations. For example, the function NOT(x) may be equivalently expressed as NAND(x,x). In the field of <a href="/facts/Digital_electronics/3kJcKbkw">digital electronic circuits</a>, this implies that it is possible to implement any <a href="/facts/Boolean_function/uT7E8pqC">Boolean function</a> using just <a href="/facts/NAND_gate/g6FUuhJT">NAND gates</a>. </p><p>The mathematical proof for this was published by <a href="/facts/Henry_M._Sheffer/YF8RpQKG">Henry M. Sheffer</a> in 1913 in the <i><a href="/facts/Transactions_of_the_American_Mathematical_Society/JmKtyCwK">Transactions of the American Mathematical Society</a></i> (Sheffer 1913). A similar case applies to the <a href="/facts/Logical_NOR/HKhNW8Qc">NOR function</a>, and this is referred to as <a href="/facts/NOR_logic/GhHdKb4q">NOR logic</a>. </p>