(Word Problem -Combinational Circuit) The list of operations for a combinational
ID: 1834750 • Letter: #
Question
(Word Problem -Combinational Circuit) The list of operations for a combinational circuit are given in the following table, where N1 and N2 are two-bit numbers, C1, C0 are control inputs, and N3 is a 4-bit number. Assume that we assign input variables AB to N1, CD to N2 and ABCD to N3. Thus if N1=2, then A=1 and B=0, etc. Also note that when the output should be negative, it is set to zero. The circuit contains one 4-bit output Z.(Z3 is the MSB.)
C1 C0 Function Comment
0 0 Z= N1 plus N2
0 1 Z= N1 minus N2 Z= 0000 if N2 > N1
1 0 Z= N'3 The One’s Complement of N3
1 1 Z= N'3 plus 1 The Two’s Complement of N3
a. Complete the following truth table.
b. Write expressions for Z3, Z2, Z1, and Z0 using little m sum of product notation.
Z3 =m
Z2 =m
Z1 =m
Z0 =m
m# C1 C0 A B C D Z3 Z2 Z1 Z0
0 0 0 0 0 0 0
1 0 0 0 0 0 1
2 0 0 0 0 1 0
3 0 0 0 0 1 1
4 0 0 0 1 0 0
0 0 0 1 0 1
6 0 0 0 1 1 0
7 0 0 0 1 1 1
8 0 0 1 0 0 0
9 0 0 1 0 0 1
0 0 1 0 1 0
11 0 0 1 0 1 1
12 0 0 1 1 0 0
13 0 0 1 1 0 1
14 0 0 1 1 1 0
0 0 1 1 1 1
16 0 1 0 0 0 0
17 0 1 0 0 0 1
18 0 1 0 0 1 0
19 0 1 0 0 1 1
0 1 0 1 0 0
21 0 1 0 1 0 1
22 0 1 0 1 1 0
23 0 1 0 1 1 1
24 0 1 1 0 0 0
0 1 1 0 0 1
26 0 1 1 0 1 0
27 0 1 1 0 1 1
28 0 1 1 1 0 0
29 0 1 1 1 0 1
0 1 1 1 1 0
31 0 1 1 1 1 1
m# C1 C0 A B C D Z3 Z2 Z1 Z0
32 1 0 0 0 0 0
33 1 0 0 0 0 1
34 1 0 0 0 1 0
35 1 0 0 0 1 1
36 1 0 0 1 0 0
37 1 0 0 1 0 1
38 1 0 0 1 1 0
39 1 0 0 1 1 1
40 1 0 1 0 0 0
41 1 0 1 0 0 1
42 1 0 1 0 1 0
43 1 0 1 0 1 1
44 1 0 1 1 0 0
45 1 0 1 1 0 1
46 1 0 1 1 1 0
47 1 0 1 1 1 1
48 1 1 0 0 0 0
49 1 1 0 0 0 1
50 1 1 0 0 1 0
51 1 1 0 0 1 1
52 1 1 0 1 0 0
53 1 1 0 1 0 1
54 1 1 0 1 1 0
55 1 1 0 1 1 1
56 1 1 1 0 0 0
57 1 1 1 0 0 1
58 1 1 1 0 1 0
59 1 1 1 0 1 1
60 1 1 1 1 0 0
61 1 1 1 1 0 1
62 1 1 1 1 1 0
63 1 1 1 1 1 1
Explanation / Answer
m# C1 C0 A B C D Z3 Z2 Z1 Z0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 2 0 0 0 0 1 0 0 0 1 0 3 0 0 0 0 1 1 0 0 1 1 4 0 0 0 1 0 0 0 0 0 1 5 0 0 0 1 0 1 0 0 1 0 6 0 0 0 1 1 0 0 0 1 1 7 0 0 0 1 1 1 0 1 0 0 8 0 0 1 0 0 0 0 0 1 0 9 0 0 1 0 0 1 0 0 1 1 10 0 0 1 0 1 0 0 1 0 0 11 0 0 1 0 1 1 0 1 0 1 12 0 0 1 1 0 0 0 0 1 1 13 0 0 1 1 0 1 0 1 0 0 14 0 0 1 1 1 0 0 1 0 1 15 0 0 1 1 1 1 0 1 1 0 16 0 1 0 0 0 0 0 0 0 0 17 0 1 0 0 0 1 0 0 0 0 18 0 1 0 0 1 0 0 0 0 0 19 0 1 0 0 1 1 0 0 0 0 20 0 1 0 1 0 0 0 0 0 1 21 0 1 0 1 0 1 0 0 0 0 22 0 1 0 1 1 0 0 0 0 0 23 0 1 0 1 1 1 0 0 0 0 24 0 1 1 0 0 0 0 0 1 0 25 0 1 1 0 0 1 0 0 0 1 26 0 1 1 0 1 0 0 0 0 0 27 0 1 1 0 1 1 0 0 0 0 28 0 1 1 1 0 0 0 0 1 1 29 0 1 1 1 0 1 0 0 1 0 30 0 1 1 1 1 0 0 0 0 1 31 0 1 1 1 1 1 0 0 0 0 m# C1 C0 A B C D Z3 Z2 Z1 Z0 Z4 32 1 0 0 0 0 0 1 1 1 1 33 1 0 0 0 0 1 1 1 1 0 34 1 0 0 0 1 0 1 1 0 1 35 1 0 0 0 1 1 1 1 0 0 36 1 0 0 1 0 0 1 0 1 1 37 1 0 0 1 0 1 1 0 1 0 38 1 0 0 1 1 0 1 0 0 1 39 1 0 0 1 1 1 1 0 0 0 40 1 0 1 0 0 0 0 1 1 1 41 1 0 1 0 0 1 0 1 1 0 42 1 0 1 0 1 0 0 1 0 1 43 1 0 1 0 1 1 0 1 0 0 44 1 0 1 1 0 0 0 0 1 1 45 1 0 1 1 0 1 0 0 1 0 46 1 0 1 1 1 0 0 0 0 1 47 1 0 1 1 1 1 0 0 0 0 48 1 1 0 0 0 0 0 0 0 0 1 49 1 1 0 0 0 1 1 1 1 1 50 1 1 0 0 1 0 1 1 1 0 51 1 1 0 0 1 1 1 1 0 1 52 1 1 0 1 0 0 1 1 0 0 53 1 1 0 1 0 1 1 0 1 1 54 1 1 0 1 1 0 1 0 1 0 55 1 1 0 1 1 1 1 0 0 1 56 1 1 1 0 0 0 1 0 0 0 57 1 1 1 0 0 1 0 1 1 1 58 1 1 1 0 1 0 0 1 1 0 59 1 1 1 0 1 1 0 1 0 1 60 1 1 1 1 0 0 0 1 0 0 61 1 1 1 1 0 1 0 0 1 1 62 1 1 1 1 1 0 0 0 1 0 63 1 1 1 1 1 1 0 0 0 1 Z3 =Sm(32,33,34,35,36,37,38,39,49,50,51,52,53,54,55,56) Z2 =Sm(7,10,11,13,14,15,32,33,3,35,40,41,42,43,49,50,51,52,57,58,59,60) Z1 =Sm(2,3,5,6,8,9,12,15,24,28,29,32,33,36,37,40,41,44,45,49,50,53,54,57,58,61,62) Z0 =Sm(1,3,4,6,9,11,12,14,20,25,28,30,32,34,36,38,40,42,44,46,49,51,53,55,57,59,61,63)
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