V2EX sum-of-products

Sum-of-products

定义 Definition

sum-of-products(乘积之和,SOP):一种常见的代数/逻辑表示形式,把表达式写成“若干个乘积项(products)相加”的形式。在布尔代数与数字电路中,通常指把逻辑函数表示为多个“与(AND)项”再用“或(OR)”连接,例如:
\[ F = (A \cdot B) + (C \cdot \overline{D}) \]
(也存在其他语境下的“乘积求和/乘积之和”用法,但数字逻辑里的 SOP 最常见。)

发音 Pronunciation

/sm v prdkts/

例句 Examples

We wrote the Boolean function in sum-of-products form.
我们把这个布尔函数写成了乘积之和(SOP)形式。

To minimize the circuit, first convert the truth table into a canonical sum-of-products expression, then simplify it with Karnaugh maps.
为了最小化电路,先把真值表转换为规范的乘积之和表达式,再用卡诺图进行化简。

词源 Etymology

该术语由数学结构直译而来:sum(和)+ of + products(乘积的复数)。在代数中,“sum of products”描述一种把表达式拆成多个“乘积项”再相加的写法;在 20 世纪的开关理论与布尔代数发展中,这种形式被广泛用于描述与实现逻辑电路,因此在数字设计教材与工程语境中固定为 SOP。

相关词 Related Words

文学与作品 Literary Works

  • Digital Design(M. Morris Mano & Michael D. Ciletti)在组合逻辑章节中使用并讲解 sum-of-products 及其规范形式与化简方法。
  • Fundamentals of Logic Design(Charles H. Roth Jr. & Larry L. Kinney)讨论从真值表到 SOP 表达、最小化与电路实现。
  • Computer Organization and Design(David A. Patterson & John L. Hennessy)在数字逻辑/组合电路相关背景中涉及 SOP 等布尔表示法。
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