Hexadecimal - Lakelands Computing

Title
Go to content
Hexadecimal
Like Binary, Hexadecimal is a number system. It was created because binary is not particularly friendly to use.

Programmers need to be able to identify and refer to specific places in the computer memory. The computer knows them by their 8 numeral binary address . Hexadecimal allows programmers to use just two numerals .

Once you are used to working with it, Hexadecimal (Hex) can be read as easily as Denary, and  you can convert between Binary and Hex quickly and easily.

Hex has 16 numerals:
As well as having different numerals that include A,B, C etc. It has different place values too.
Place value1,000
10^3
100
10^2
10
10^1
1
10^0
Numerals3419

(3*1000)+ (4*100) + (1*10) + (9*1)
Place value4096
(16^3)
256
(16^2)
16
(16^1)
1
(16^0)
Numerals114A
(1*4096)+(1*256)+(4*16)+(10*1). Remember A is 10
  • Denary has place values of 1, 10, 100, 1000

  • These are powers of 10.

  • This number is 3419
  • Hex has place values of  1, 16, 256, 4096

  • These are powers of 16.

  • This number is 4426 (Den)
To convert from Hexadecimal to Denary
Step
Outcome
Explanation / Notes
1) Write down the Hex place values
256
16
1
2) Write the Hex value into the columns4A7
3) Convert any Letters to their number equivalent
4107A is 10
4) Write down the sums to multiply each numeral by its place value
4 * 256
10 * 16
7 * 1

5) Calculate the sums1024
160
7
4*256 =1024
10 * 16 = 160
7 * 1 = 7
6) Add up the your answers to get final answer11911024 + 160 +7 = 1191
To convert from Denary to Hexadecimal
Step
Outcome
Explanation / Notes
1) Take the Denary number171
2) Divide it by 16 (it helps to know your 16 times table here)10 r 11171/16 = 10 remainder 11
3) Write down the remainder as its Hex equivalent
BThe remainder is 11
11 in Hex is B
4) Take the quotient - the main part (the 10),

If it is less than 16:
  • Write down the remainder as its Hex equivalent

  • If it is more than 16:
    • Repeat steps 2, 3 and 4 eg divide by 16 etc.. until the quotient (main bit) is below 16, and has been written down in Hex
A10 is less than 16
10 is A in Hex
5) Final answer AB
All Text copyright Lakelands Academy & Mr T Purslow 2020.
All images copyright free / creative commons unless otherwise stated.
You are welcome to use under a Creative Commons Attribution-nonCommercial-ShareAlike License.
All Text copyright Lakelands Academy & Mr T Purslow 2020.  All images copyright free / creative commons unless otherwise stated. You are welcome to use under a Creative Commons Attribution-nonCommercial-ShareAlike License.
All Text copyright Lakelands Academy & Mr T Purslow 2020.  All images copyright free / creative commons unless otherwise stated. You are welcome to use under a Creative Commons Attribution-nonCommercial-ShareAlike License.
Back to content