Chapter 1 - Data Representation

Question 1

Data representation

Answer 1

Methods used internally to represent information stored in a computer

Question 2

3 main coding systems

Answer 2

• American Standard Coded for Information Interchange (ASCII)
• Extended Binary Coded Decimal Interchange Code (EBCDIC)
• Unicode

Question 3

Binary System

Answer 3

• Computers are digital
  
  • Only 2 discrete states: 0(off) or 1(on)
  • Each digit is known as a bit (binary digit)

Question 4

Data representation

Answer 4

• 8 bits -> 1 byte
• 1 byte can represent 2^8 = 256 pieces of information
• More bytes - represent numbers, characters, etc.

Question 5

Data types

Answer 5

• Vary in
  
  • Word length - number of bits used
  • Representation
    
    • Fixed-point - integer or long
    • Floating-point - float or double

Question 6

Fixed-point representation

Answer 6

• Used for integer or long numbers
• 3 systems to represent numbers:
  
  • Sign-and-magnitude
  • 1’s complement
  • 2’s complement

Question 7

Sign-and-magnitude

Answer 7

• leftmost bit - sign; remaining bits - magnitude

* Just change the sign bit and keep the magnitude to show the negative value

Question 8

1’s complement

Answer 8

• Negative values - complement each bit of the corresponding positive number

Question 9

2’s complement

Answer 9

• Negative values - do the 1’s complement first by complement each bit of the corresponding positive number. Add one to the 1’s complement.

Question 10

IEEE

Answer 10

Institute of Electrical and Electronic Engineers

Question 11

Floating-point representation

Answer 11

• According to the international Institute of Electrical and Electronic Engineers(IEEE), numbers are represented in the normalized form

Question 12

Types of errors

Answer 12

• Mistakes
• Random error
• Truncation error
• Round off error
• Propagated error

Question 13

Mistakes

Answer 13

typographical errors entered with program or maybe running the program using the wrong data etc.

Question 14

Random errors

Answer 14

caused by random fluctuations in electronics due to for example power surges.

Question 15

Truncation errors

Answer 15

Due to simplification of mathematics to make it easy to solve the problem

Question 16

Round off errors

Answer 16

Since most numbers are represented with imprecision by computers (and general restrictions), this lead to a number being lost.

Question 17

Propagated errors

Answer 17

• Error in later steps of a program due to an earlier error
• Critical as errors may be magnified causing results to be invalid
• Stability of the program determines how errors are propagated

Question 18

Parity bit

Answer 18

• Odd
• Even

• If a computer uses even parity, the total number of 1-bits should be even. If the total is odd, then there is an error

Question 19

Precision

Answer 19

• Consequence of storage scheme - limit to precision
• If the mantissa of the numbers are different, the exponent of the smaller number is made larger while the mantissa is made smaller until they are same(shifting bits to right while inserting zeros).