Candidates should be able to:
a)
Convert positive denary whole numbers (0-255) into 8-bit
binary numbers and vice versa
b) Add two 8-bit binary integers and explain overflow
errors which may occur
c) Convert positive denary whole numbers (0-255) into 2digit hexadecimal numbers and vice versa.
d) Convert between binary and Hex equivalents of the
same number
e) Explain the use of Hex numbers to represent binary
numbers
Hexadecimal Numbers
 Hexadecimal is the name given to numbers using base 16
 Decimal numbers 10 – 15 are represented using letter A – F
 16 values so base 16
Hexadecimal
 Used in computing as it is a much shorter way of
representing a byte of data. Binary data = 8 digits,
Hexadecimal data = 2 digits
E.G. 11111111 = FF
 Largest byte value is 255 and hexadecimal can
represent up to that number
Binary to Hexadecimal
 HEX is used to express binary numbers in a more
compact form
 HEX numbers run from Zero to F (15 decimal)
 15 decimal = 1111 (nibble) = F (Hex)
Binary to Hexadecimal
 Example 1 – 11011110 as Hex number
 Split number into 2 nibbles (1101…..1110)
 Convert number to decimal
1101 = 13
 1110 = 14
Convert number to Hex
 13 = D
 14 = E
11011110 = DE (Hex)
Hexadecimal to Binary
 Example 1 – E3 as binary number
 Take 1st Hex digit – convert to binary nibble
 3 Hex = 3 decimal = 0011 binary
 Take 2nd hex digit – convert to binary nibble
 E Hex = 15 decimal = 1110 binary
 Put the 2 nibbles together
1110 0011 (E3 in binary)
Decimal to Hexadecimal conversion
Example 1 – 55 as Hex number
 Put headings 128 64 32 16 8 4 etc
Write out binary number (55) 00110111
 Split into 2 nibbles: 0011…0111
0011 = 3
 0111 = 7
55 = 37 (Hex)
Decimal to Hexadecimal conversion
Example 2 – 17 as Hex number
 Put headings 128 64 32 16 8 4 etc
Write out binary number (17) 00010001
 Split into 2 nibbles: 0001…0001
0001 = 1
 0001 = 1
17 = 11 (Hex)
Have a go at these
http://templehouse.me.uk/gcsecomputing/
BinaryHexConversion.html
OR – MUCH HARDER
http://people.sinclair.edu/nickreeder/Flash/
binHex.htm
Have a go at the Test