课程名称︰交换电路与逻辑设计
课程性质︰必修
课程教师︰简韶逸
开课学院：电机资讯学院
开课系所︰电机工程学系
考试日期（年月日）︰103/10/23
考试时限（分钟）：50分钟
试题 :
Switching Circuit & Logic Design, Fall 2014
Quiz # 1(2:20pm ~ 3:10pm, 2014/10/23)
Problem 1: (32 points)
Consider two 6-bit numbers A = 100110 and B = 001011.
(A) Represent A and -B in 8-bit words for signed magnitude numbers A and B.(8%)
(B) Represent -A and -B in 8-bit words for 2's complement numbers A and B.(8%)
(C) Compute A ÷B in binary for (6-bit) unsigned numbers A and B.(8%)
(D) Compute A - B for (6-bit) 1's complemen numbers A and B.Does any overflow
occur?(8%)
Problem 2: (18 points)
Consider three Boolean functions f, g, and h over variables {A, B, C} with
f = g □ h, where "□" is some Boolean operator. Suppose that function f is
specified by the following truth table, and g = A' + B'.
┌───┬──┐
│ ABC │ f │
├───┼──┤
│ 000 │ 0 │
│ 001 │ 1 │
│ 010 │ 0 │
│ 011 │ 1 │
│ 100 │ 0 │
│ 101 │ 1 │
│ 110 │ 1 │
│ 111 │ 0 │
└───┴──┘
(A) For □ being an XOR(⊕), what are the all possible solutions to function h
if h does exist? If h does not exist, what are the minterms(assignments to
variables A, B, C) of f that are in conflict?(9%)
(B) For □ being an AND(．), what are the all possible solutions to function h
if h does exist? If h does not exist, what are the minterms(assignments to
variables A, B, C) of f that are in conflict?(9%)
Problem 3: (20 points)
F is a four-variable function, where:
F(a,b,c,d) = ΠM(0,1,2)．ΠD(4),
(A) What is the minterm expansion of F(a,b,c,d)?(10%)
(B) Write F(a,b,c,d) in a minimum sum-of-product form. Please note that the
K-map method cannot be used in the answer.(10%)
Problem 4: (30 points)
For H(a,b,c) = a⊕b⊕c:
(A) What is H'(a,b,c) in the minimum sum-of-product form?(15%)
(B) What is the value of H'(1,1,0)?(5%)
(C) If you are only allowed to use a, b, c, 0 or 1 as the inputs (a', b' and
c' are not available), please design a circuit to realize H'(a,b,c) in
using only two-input exclusive-OR gates.(10%)