131 Week 2 - Information Coding

Question 1

Why do we need information coding

Answer 1

To allow for more complex data and data types to exist but still be coded into (or represented as) something that is cheap and easy to store and process.
Computer hardware handles data types and data as small positive whole numbers.

Question 2

ASCII

Answer 2

American Standard Code for Information Interchange
Defines 128 (2^7) symbols - 7 bit binary.

Question 3

How can negative numbers be represented?

Answer 3

Sign and magnitude, excess n

Question 4

Sign and magnitude

Answer 4

A character is used to represent if a number is negative or positive. It is then followed by the magnitude of the number.
It works however a column is sacrificed and 0 can be represented twice as it can be positive or negative.

Question 5

Excess n

Answer 5

Uses n as a new value for 0. Any positive number is added to the n and any negative number is subtracted from the n.
e.g., 150 in excess 5000 is 5150. -25 in excess 5000 is 4975.
It doesn’t use an extra column and has a single value for 0.

Question 6

How can decimal numbers be represented?

Answer 6

Fixed point, floating point

Question 7

Fixed point decimals

Answer 7

Some columns are reserved for the fractional part of a number.
However this is not a very efficient use of columns.

Question 8

Floating point decimals

Answer 8

Trades precision for range by using a mantissa and exponent to represent numbers. Mantissa and exponent are represented with sign and magnitude.
Mantissa * Radix^exponent

Question 9

Radix

Answer 9

The amount of characters a number system uses to represent numbers.
Also called the base

Question 10

Denary (decimal)

Answer 10

A way of representing numbers using 0-9
Radix (base) 10

Question 11

Binary

Answer 11

A way of representing numbers using 0,1
Radix (base) 2

Question 12

Octal

Answer 12

A way of representing numbers using 0-7
Radix (base) 8

Question 13

Hexadecimal

Answer 13

A way of representing numbers using 0-9, A-F
Radix (base) 16

Question 14

Addition rules for adding binary numbers

Answer 14

0+0=0
1+0=1
0+1=1
1+1=0 carry 1
1+1+1=1 carry 1

Question 15

Problems with sign and magnitude and excess n arithmetic

Answer 15

Sign and magnitude: doesn’t deal with overflow
Excess n: x – y ≠ x + (-y)
Would need extra hardware to be able do subtraction as well as addition for excess n. This would be less space and cost effective.

Question 16

2’s Complement

Answer 16

A way of representing negative numbers where they can be added and subtracted from each other.

Question 17

Converting +ve to -ve in 2’s complement

Answer 17

Start with the equivalent positive number
Flip all bits (0 to 1, 1 to 0)
Add 1 to the number, ignoring overflow.

Question 18

IEEE 754 Standard floating point

Answer 18

Mantissa is coded in sign and magnitude
Exponent is coded in excess n
Has multiple precisions: half, single, double, quadruple.

Question 19

Single precision IEEE 754

Answer 19

Uses 32 bits overall
First bit is used for mantissa sign bit
Next 8 bits used for exponent in excess 127
Remaining 23 bits used for mantissa magnitude.

Question 20

How is the mantissa normalised for IEEE 754

Answer 20

Mantissa is always normalised to start as 1.xxxxx
The first bit then does not has to be stored as it will always be 1. and can just be assumed to be so.