Introduction to Digital Circuit Design HOMEWORK # 1

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ECE 2029 Introduction to Digital Circuit Design
HOMEWORK # 1

Student Name:
Date:
Problems Score Instructor/TA’s Comments
1) /10
2) /10
3) /20
4) /40
5) /10
6) /10
Total /100
TA’s/Instructor’s Signature: Date:
Important (TIPS)
1. Print this HW sheet and do your work here. Staple extra sheet in case you need more space
to show your work.
2. Show all the process work neatly, don’t just jump to answer. Partial credit may be given.
Box/highlight your answer.
3. Read the problem carefully, don’t assume. Look for the simple, straightforward way to solve
the problem. Don’t overdo yourself.
4. To make the grading easier, please return your homework on this problem sheet.
5. If you need to use an extra piece of paper, please staple it on and number your solutions just
like below!
6. Please turn it into the ECE2029 box located at the ECE department office AK202 above the
shelf just when you walk-in. Don’t forget to put your mailbox number.
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Problem 1 - 10 points total
Express the numbers given, in binary form (using the ordinary, and NOT 2’s complement, positive only
binary positional number system)
(a) (3D)16 (b) (63)8
(c) (AC)16 (d) (24)5
(e) (2345)16 (f) (3255)8
(g) (ACFE)16 (h) (29)
10
(i) (C4D278)16 (j) (4156)8
Problem 2 -20 points total
Express the numbers given, in binary form (using the ordinary, and NOT 2’s complement, positive only binary
positional number system). Perform the conversion using the method of repeated division or repeated
multiplication as appropriate, showing all steps.
(a) (3.703125)
10
(b) (12.5078125)10
 ( )2
( ) 2
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Problem 3 -20 points total
Convert the following numbers (which are given in ordinary “unsigned” positional number system
and not 2’s complement format) to decimal values:
(a) (C.82)16 (b) (14.404)8
(c) (11101.110011…)2
(d) (11001.0001)2
( ) 10 ( ) 10
( ) 10 ( ) 10
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Problem 4 – 40 points total
(a) Complete the table below: [5 pts]
Range: n-bit unsigned and signed (2’s complement) numbers
2-bit 3-bit 4-bit 8-bit 16-bit
Unsigned
2’s Complement
(b) Add -118 and -32 firstly using 8-bit 2’s complement arithmetic and then using 16-bit 2’s
complement arithmetic, Comment on the results. [20 pts]
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(c) Perform the indicated arithmetic on the following signed two’s complement binary numbers.
[15 pts]
Your answer should show the two’s complement binary result; also indicate if each result is positive
or negative or overflowed (writing out “positive”, “negative” or “overflow” next to the binary
answer) and then follow with the decimal value of the result if there was no overflow. Do not extend
(add any additional length) to these representations, but rather use a binary number word size equal
to those found in each problem statement.
(i) 01011011 + 11100101 (ii) 01001 -01110
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(iii) 1111 + 1100
Problem 5 – 10 points total
(a) Perform the following decimal arithmetic problems by first converting the numbers to binary, 2’s
complement form (using a 7 bit word in every case). Then perform the 2’s compliment
addition. Show the result in binary indicating as in the problem above whether each result is
positive or negative or overflowed (writing out “positive”, “negative” or “overflow” next to
the binary answer) and then follow with the decimal value of the result if there was no
overflow.
(i) 13 – 9 (ii) –13 – 13
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Problem 6 – 10 points total
Fill the table below:
4-bit signed binary number comparison
Decimal Signed
Magnitude
Signed 1’s
Complement
Signed 2’s
Complement
+7
+6
+5
+4
+3
+2
+1
+0
-0
-1
-2
-3
-4
-5
-6
-7