ECE 171 DIGITAL CIRCUITS PSU
HM HW 1
(1/15/2016)
Due Date:
Total Points:
Thursday 1/21/2016 by start of class
100
General Rule: Write your homework using a word processor or similar electronic tool, then submit the file to the grader via email by the deadline, cc Herb. Use email subject line “ ECE 171 HW 1 . . .
”.
Problem 1: Convert the decimal numbers below to their binary equivalent:
= a.) 13 b.) 19 c.) 42 d.) 73 e.) 106
=
=
=
= f.) 44 g.) 163 h.) 52 i.) 105 j.) 15
=
=
=
=
=
Problem 2: Convert the binary numbers below to their equivalent hexadecimal representation: a.) 00010001 = b.) 01011001 = c.) 10010110 = d.) 01111010 = e.) 11011100 = f.) 10111111 = g.) 1011011011 = h.) 010111111011 = i.) 111111111111 = j.) 101010101010 =
Problem 3: Convert hexadecimal numbers to their equivalent binary representation: a.) A = b.) FF c.) AB d.) 10 e.) 11 f.) 1F
=
=
=
=
=
Problem 4: Convert the binary numbers below to their equivalent base 8 and 16 representation: a.) 1111111111
2
= b.) 1000100010
2
= c.) 1000001
2
= d.) 101000111
2
= e.) 1000000001
2
=
Problem 5: F1() is a Boolean function of variables a, b, c, and d. Value 1 stands for Boolean true, 0 for false. A value tagged ’ negates. For example, a’b means: a not, and b, with the logical and implied. (In other texts, logical and is expressed via the * operator; not in this homework. In Verilog,
1
HW 1

ECE 171 DIGITAL CIRCUITS PSU
HM HW 1 negation is expressed via ! for logical and ~ for bitwise negation; not here.) Function f1() = a’b’c’d’
+ ab’c’d’ + a’b’cd’ + ab’cd’ + a’bc’d + a’bcd + abc’d + abcd. Simplify f1() to a minimal SOP form, but start out by writing f1() as a sum of all 8 individual true values; then minimize.
c c
1 0 0 1
0 1 1 0 b a 0 1 1 0 b a 1 0 0 1
d d
Table 1: Function f1() of 4 Boolean variables a, b, c, d
Step 0: all 8 terms: f1() =
Step 1: or-terms simplified:
Step 2: partial or-terms simplified:
Problem 6: a.) What constitutes overflow on a digital computer? b.) How is overflow detected on a two’s-complement computer? (Note signed is implied!) c.) How is overflow detected, when 2 unsigned binary numbers are added on a digital computer? d.) What is an advantage of two’s complement architecture? e.) What is irregular in two’s-complement arithmetic? a.) : b.) : c.) : d.) : e.) :
Problem 7: Given a binary computer with a word size of 8 bits, convert all the following decimal numbers to sign-magnitude representation (SM), to one’s complement representation (OC), and to two’s complement representation (TC):
2
HW 1

ECE 171 DIGITAL CIRCUITS PSU
HM HW 1 a.) 28 = b.) c.) d.) e.)
37 =
-28 =
-17 =
-35 =
Problem 8: What is the hex (short for hexadecimal) representation of the ASCII string: “ECE 171”?
For example the hex representation of string “AB” is 0x41 0x42, or simply 41 42, base 16 implied
Problem 9: Explain, what is a combinational logic circuit, and what is a sequential logic circuit.
Problem 10: Explain Gray Code (GC). What is the purpose of encoding binary states using GC? Does the number of states in GC equal the number of states in regular numeric, binary encoding? State an example, where GC exhibits some advantage.
Problem 11: Convert each of the following hexadecimal numbers to its equivalent binary representation.
C
16
= a.) b.) c.) d.)
A1
32
123
16
16
16
=
=
= e.) BFF
16
=
Problem 12: Convert each of the following binary numbers to its equivalent hexadecimal and octal representation. a.) b.)
10000001 =
101000111 =
Problem 13: Convert another set of hexadecimal numbers to decimal. a.) b.) c.) d.) e.)
10
1A
BA
EE
7C
16
16
16
16
16
=
=
=
=
=
Table 1: Distribution of Points
#
1
2
Convert to binary
Convert to hex
Problem Points
10
10
3
HW 1

ECE 171
HM
3
4
5
6
7
8
9
10
11
12
13
DIGITAL CIRCUITS
HW 1
Convert to binary
Convert to octal and hex
Boolean expression simplification
Overflow
Arithmetic options
Bit-wise equivalent of ASCII string
Combinational vs. sequential circuit
Gray Code
Convert to base 2
Convert to base 16 and 8
Convert to base 10
Total
10
10
10
10
10
5
5
5
5
5
5
100
PSU
4
HW 1