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University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 1/8 Problem 1:
VCCC_H INPUT
VCCB_H INPUT
VCCC_H INPUT
VCCA_H INPUT
VCCA_H INPUT
VCCB_H INPUT X_HOUTPUT
Y_HOUTPUT
NOT
13
NOT
25
NOT
15NOT
21
NOT
12
NOT
14
OR2
17
OR2
24
OR2
18
OR2
16AND2
19
AND2
23
AND2
22
AND2
26
X = /(/A + B) * (B + /C)1 a)
Y = (A + /B) * /(/B * /C + B * C)1 b)
Problem 2:
VCCC_L INPUT
VCCA_L INPUT
VCCB_H INPUT
VCCC_H INPUT
VCCB_H INPUT
VCCA_L INPUT
X_HOUTPUT
Y_HOUTPUT
OR2
35
AND2
30
AND2
33
AND2
31
NOR2
50
NOR2
57
BOR2
54BAND2
56
2 a)
2 b)
X = /(/A + B) * (B + /C)
Y = (A + /B) * /(/B * /C + B * C)
Problem 3:
VCCC_L INPUT
VCCD_H INPUT
VCCA_L INPUT
VCCB_H INPUT
X_LOUTPUT
NOT
68
NOR2
60 BOR2
59
BAND2
58B
/D
21'02
3
00
40204
/A/(/A + B)
/(/A + B)
02
02
2
31
5
6
C
/[ /(/A + B) * C ]1
2
/{ /[ /(/A + B) * C ] + /D }
Problem 4: a) 12-bit unsigned binary = 1010 1111 1111 = 2048+512+255 = 2815
b) 12-bit sign magnitude = -(512+255) = -767 c) 12-bit 1’s complement = -(0101 0000 0000) = -(1024+256) = -1280 d) 12-bit 2’s complement = -(0101 0000 0001) = -(1024+256+1) = -1281 e) 12-bit BCD = not a valid BCD number
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 2/8 Problem 5:
3 bit signed 3 bit 1’s compl 3 bit 2’s compl 000 0 0 0 001 1 1 1 010 2 2 2 011 3 3 3 100 (-)0 -3 -4 101 -1 -2 -3 110 -2 -1 -2 111 -3 (-)0 -1
Problem 6: 1 1001 25 * 1 0110 *22 11 0010 50 110 01 50 1 1001 550 10 0010 0110 Problem 7:
a) 1001 0101 149 + 0111 1111 +127
1 0001 0100 276
b) 8 bit 2’s complement: 1001 0101 -107 + 0111 1111 +127
(1) 0001 0100 20 Ignore the(1)
c) 8 bit signed complement: 1001 0101 -21 + 0111 1111 +127
106 Since the first number is negative and the second number is positive, I’ll subtract the first number (unsigned) from the second.
0111 1111 +127 - 0001 0101 -21
0110 1010 106 Since the answer is positive, I’ll leave the sign bit as a zero. d) Problem a) is not valid 276 > 2^8 (256). Problems b) and c)
are valid.
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 3/8
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 4/8
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 5/8
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 6/8
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 7/8
Roth 6th: 1.17
Roth 6th: 1.20
Roth 6th: 1.32
University of Florida EEL 3701 Dr. Eric M. Schwartz Department of Electrical & Computer Engineering Homework 2 Solutions Page 8/8
Roth 6th: 1.34