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"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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