Exercise on Data Representation

1.

Fill in the table below by converting between the various number systems:

 Decimal Binary Hexadecimal 201 100110 B6

2.

Fill in the table below by converting between the various number systems:

 Decimal Binary Hexadecimal 157 11011011 2E

3.

The numbers 71 and -62 are stored in registers A and B in two’s complement form. Demonstrate how the computer works out 71-62 in binary.

4.

Name one other character set (besides ASCII) that is in more widespread use nowadays. Why has this character set become more common?

5.

Consider an 8-bit unsigned register.

a)   What is the range of decimal values that can be stored in this register?

b)  Write down the binary contents of this register when it is storing the decimal number 109. Show your working.

c)   Express the contents of this register in hexadecimal. Show your working.

d)  Given that the ASCII code for ‘a’ is 97, write the character that this register will be storing if it were representing text in ASCII. Show your working.

6.

Consider an 8-bit two’s complement register A which currently contains the binary value 00101111.

a)   Determine the value of the register in decimal.

b)  Determine the value of the register in hexadecimal.

c)   Determine the largest positive value that this register can store.

The contents of the register are shifted by one bit to the left.

d)  State which mathematical operation this action corresponds to.

The contents of the register are now complemented.

e)   Perform the complementation of the contents of the register.

f)    State which mathematical operation this action corresponds to.

Another identical register B contains the binary value 01101000

g)   State what happens if the contents of A and B are added together.

h)  Perform the addition between the contents of register A and B.

7.

A custom text encoding system utilises 6 bits to represent each character.

a)   State the amount of different characters that can be represented using this system.

b)  Assuming all letters are encoded sequentially, if the letter ‘j’ is represented by the decimal number 35, state which letter is represented by the binary number 101000.

c)   State what the following abbreviations stand for:

i)    ASCII

ii)   UTF

d)  Answer True (T) or False (F) to the following:

 ASCII has more control characters than printable characters. Extended ASCII can only represent words in the English language. ASCII can represent at most 256 characters. UTF was meant to be able to represent characters from any language.

8.