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Chapter

ITEC 1000 Chapter Notes -Radix Point, Scientific Notation, Radix


Department
Information Technology
Course Code
ITEC 1000
Professor
Peter Khaiter

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AP/ITEC1000 Sections A and B
"Introduction to Information Technologies"
Fall 2011
Assignment # 2
Answers and Solutions
1)
a) Convert 121 to its binary representation: 12110 = 011110012. Positive numbers are always
represented by themselves.
The answer: 01111001
b) Convert -121 to its binary representation: -12110 = -011110012. Using the second method
for negative numbers, invert and then add 1.
The answer: 10000111
c) Convert 54 to its binary representation: 5410 = 001101102. Positive numbers are always
represented by themselves.
The answer: 00110110
2) Yes. The four least significant bits of the EBCDIC code match the four least significant digits
of ASCII.
3) Between -79999 and +79999. This is because 20 bits provide five four-bit locations. The
lowest (right most) and three middle 4 bit groups can each store any number from 0 to 9. In the
highest (left most) 4 bits, one bit is used for the sign, leaving 3 bits for digits. These 3 bits can
accommodate numbers between 0 and 7.
4)
a) 15765 is a positive number and is represented by itself
99999 - 8773 = 91226

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b) 15765
+91226
106991 add the carry into the result
+ 1
06992
The leading digit in the complement is 0. Therefore, it represents a positive decimal
number: 6992.
c) There was no overflow condition because the inputs in the sum have opposite signs and
overflow cannot occur.
There was a carry condition because in the result, the number of digit exceeded the
specified number (i.e., five) and the carry was added to the result.
d) 15765 is a positive number and is represented by itself
100000 - 8773 = 91227
e) 15765
+91227
106992 Ignore the carry and the result is: 6992
f) Diminished radix complement arithmetic requires an additional step of adding the carry
bit to the result.
Radix complement arithmetic does not require this step, because the carry is simply
ignored. The latter is easier.
5) Replace each decimal digit by its 4-bit BCD representation and add the corresponding sign
pattern in the low-order bits.
a) -924 = 1001001001001101 b) 80356 = 100000000011010101101111 c)
+981 = 1001100000011100
6)
a) The leading digit is between 0 and 4 and, therefore, represents a positive number. Positive
numbers are represented by themselves.
The answer: 3589
b) The leading digit is between 5 and 9 and, therefore, represents a negative number. To get
its magnitude, subtract the complement from the base:
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