Computer Science - 3 Data Representation - 1 Units and Binary Numbers & 2 Binary Arithmetic and Hexadecimal

1 bit

a single 1 or 0

1 byte

8 bits

1 nibble

4 bits / 1/2 byte

Order of prefixes [4]:

- kilo
- mega
- giga
- tera

One character of text:

1 byte

A full page of text:

30 kB

One small digital colour photograph:

3 MB

Music CD capacity:

650 MB

DVD capacity:

4.5 GB

Hard disc capacity:

1 TB

Most significant bit (MSB)

the leftmost bit in a binary number - which has the highest value

Least significant bit (LSB)

the rightmost bit in a binary number - which has the lowest value

The number of combinations from n bits =

2ⁿ

Hexadecimal

a number system that uses base 16

0 - 15 in hexadecimal =

0 - 9 and A - F

Hexadecimal to decimal conversion [2]:

- multiply value of left digit by 16
- add value of right digit

Decimal to hexadecimal conversion [2]:

- divide using integer division by 16 (value = left digit)
- remainder = right digit

Binary to hexadecimal conversion [3]:

- divide 1 byte into two nibbles (left and right)
- convert the value of each nibble to hexadecimal digits
- combine the two

Hexadecimal to binary conversion [2]:

- represent each digit in turn as 4-bit numbers
- combine them

Advantages of hexadecimal [4]:

- simpler to remember
- quicker to write or type
- less likely to make error
- easy to convert between hex and binary

Rules of binary addition:

- 0 + 0 = 1
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0 (carry 1)
- 1 + 1 + 1 = 1 (carry 1)

1 + 1 + 1 + 1 = ? [3]

- 4
- 100
- 1 carried over by 2

Overflow error

error from attempting to represent a number that is too large.

A right logical shift causes:

a division by 2 (if float, round down)

A left logical shift causes:

a multiplication by 2