SLR 2.6 Data representation

Question 1

What is binary?

Answer 1

Binary is a number system with two possible values for each digit: 0 and 1 (base 2).
In computing binary is used for digital encoding system where there are exactly two possible states e.g. switches and transistors are either on or off, magnetic storage can point north or south, optical storage used pits and lands, solid state storage has trapped electrons in gates or it doesn’t.

Question 2

What is hexadecimal?

Answer 2

A number system that uses 16 rather than 10 as its base. The 16 hexadecimal digits are 0 to 9 then A to F.

Question 3

What is denary?

Answer 3

A number system that uses 10 as its base. The 10 denary digits are 0-9.

Question 4

What is a character set?

Answer 4

The set of symbols that may be represented by a computer. These symbols, called characters, can be letters, numbers, and non-alpha-numeric characters such as punctation marks (! , . ) and ‘special characters’ e.g. & * @ # $ etc. In larger character sets such as Unicode emojis and characters from other languages e.g. Chinese can also be represented.

Question 5

What is ASCII?

Answer 5

A character set devised for early telecommunication systems but proved to be ideal for computer systems. ASCII codes use 7-bits giving 32 control codes and 96 displayable characters (the 8th bit is often used for error checking).

Question 6

What does ASCII stand for?

Answer 6

America Standard Code for Information Interchange

Question 7

What is UNICODE?

Answer 7

A standard character set that replaces the need for all the different character sets. It incorporates characters from almost all the world’s languages. It is a 16-bit extension of ASCII.

Question 8

Put these in order:

nibble, byte, bit, petabyte, megabyte, gigabyte, kilobyte, terabyte,

Answer 8

bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte, petabyte

Question 9

Convert the following 8 bit binary number into denary:

10100011

Answer 9

128 + 32 + 2 + 1 = 163

Question 10

Convert the following hexadecimal number into denary:

CC

Answer 10

Since hexadecimal C is the equivalent of 12 and the positions from right to left in hexidecimal are units then 16s we have:

16x12 + 12 = 204

Question 11

Convert the following 8 bit binary number into hexadecimal:

01011010

Answer 11

To work out hexadecimal from binary split the 8 bit byte into two nibbles and convert each value into a hexadecimal value:
0101 = 5 1010 = A
so 01011010 = 5A

Question 12

Convert the following hexadecimal number into 8 bit binary:

B7

Answer 12

To work out an 8 bit binary number from a hexadecimal number split the hexadecimal number into two values and convert each into a nibble in binary (remember that hexadecimal goes from 0 to 9 and then from A to F):
B = 1011 7 = 0111
So B7 = 10110111

Question 13

Convert the following denary value into hexadecimal:

121

Answer 13

The value of the positions in hexadecimal from right to left are units, 16s (then 16 square, 16 cubed etc.) so to work out the hexadecimal value first do integer division by 16 (that is divide by 16 and ignore any remainder)
121 // 16 = 7 (7 x 16 = 112)
then do your value modulus 16 (i.e. find the remainder)
121 % 16 = 9
Finally put the two parts together:
121 in denary is 79 in hexadecimal

Question 14

Convert the following denary number into 8 bit binary:

122

Answer 14

First remember the values of the positions from right to left in binary goes units, 2s, 4s, 8s, 16s, 32s, 64s, 128s
Then work out how many of each you can have:
128 64 32 16 8 4 2 1
0 1 1 1 1 0 1 0

Question 15

What is the result of adding the following bits together:
0 
0 +
\_\_\_
\_\_\_

Answer 15

0

Question 16

What is the result of adding the following bits together:
0 
1 +
\_\_\_
\_\_\_

Answer 16

1

Question 17

What is the result of adding the following bits together:
1 
1 +
\_\_\_
\_\_\_

Answer 17

0 carry 1

Question 18

What is the result of adding the following bits together:
1 
1 +
\_\_\_
\_\_\_
1

Answer 18

1 carry 1

Question 19

What is the result of adding the following 4 bit numbers together
1 0 1 1
00 1 1
\_\_\_\_
\_\_\_\_

Answer 19

1 0 1 1
00 1 1
\_\_\_\_
1 1 1 0
\_\_\_\_
  1 1

Question 20

What is the result of adding the following 4 bit numbers together
1 0 1 1
1 0 1 1
\_\_\_\_
\_\_\_\_

Answer 20

This results in an overflow error as the result cannot be shown in just 4 bits. There is a carry forward which cannot be processed and causes the overflow error:

  1 0 1 1
  1 0 1 1
  \_\_\_\_
  1 1 1 0 
  \_\_\_\_
1   1 1