问几个物理问题电学方面的1.(CanonicalForms)Considerthefunction:f(A,B,C,D)=∑m(0,1,2,7,8,9,10,15)(a)WritethisasaBooleanexpressionincanonicalmintermform.(b)Rewritetheexpressionincanonicalmaxtermform.(c)Writethecomp

Question

问几个物理问题电学方面的
1.(Canonical Forms) Consider the function:f (A,B,C,D) =∑m(0,1,2,7,8,9,10,15)
(a) Write this as a Boolean expression in canonical minterm form.
(b) Rewrite the expression in canonical maxterm form.
(c) Write the complement of f in “little m ” notation and as a canonical minterm
expression.
(d) Write the complement of f in “big M ” notation and as a canonical mexterm
expression.
2.(Boolean Simplification) Using K-maps,find the following:
(a) Minimum sum-of-products form for the function and its complement given in
this HW No.1.
(b) Minimum product-of-sums form for the function and its complement given in
this HW No.1.
3.(Boolean Simplification) Use K-maps and Boolean equality to simplify the
following functions in the sum-of-products form.How many literals appear in
your minimized solutions?
(a) f (X ,Y,Z) =∏M(0,1,6,7)
(b) f (W,X ,Y,Z) =∏M(1,3,7,9,11,15)
(c) f (A,B,C,D) =∑m(0,2,4,6)
4.(Boolean Simplification) Determine the minimized realization of the following
functions in the sum-of-products form:
(a) f (W,X ,Y,Z) =∑m(0,2,8,9) +∑d(1,3)
(b) f (W,X ,Y,Z) =∑m(1,7,11,13) +∑d(0,5,10,15)
(c) f (A,B,C,D) =∑m(1,2,11,13,14,15) +∑d(0,3,6,10)
(d) f (A,B,C,D) =∏M(2,5,6,8,9,10) ∗∏D(4,11,12)
5.(Laws and Theorems of Boolean Algebra) Simplify the following expressions using
the laws and theorems of Boolean algebra:
(a) W(A,B,C) = ABC + ABC + ABC + ABC
(b) X (A,B,C) = ABC + ABC + ABC + ABC
(c) Y(A,B,C,D) = ABCD + ABCD + ABCD + ABCD + ABCD + ABCD
6.Use K-maps on the expressions of this HW No.5.Show your work in K-map form.
(a) Find the minimized sum-of-products form.
(b) Find the minimized product-of-sums form.
(c) Find the minimized sum-of-products form of the function’s complement.
(d) Find the minimized product-or-sums form of the functions complement.

Answer 1

这是数字逻辑,不是电学.题目很简单啊,让你在和之集（product of sums)与集之和（sum of products)间转化,用卡诺图化简.