Name:

Convert Denary to Binary (and back again)

Denary: This is the base 10 system, this means that we use 10 symbols to represent the numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and we use units, tens and hundreds , the number 217 can be shown as:

100 / 10 / 1
2 / 1 / 7

Binary: This is the base 2 system; there are only 2 symbols (0 and 1):

128 / 64 / 32 / 16 / 8 / 4 / 2 / 1
1 / 1 / 0 / 1 / 1 / 0 / 0 / 1

Question: What denary number is shown above in binary (11011001)?

For the GCSE Computing course you need to be able to:

“Convert positive denary numbers 0 – 255 into 8 bit binary numbers and vice versa”

There are 2 easy methods to convert denary (base 10 ) to binary (base 2):

Convert binary (base 2) to denary (base 10):

Put the binary number into the columns and add up the value of the columns with 1 in them:

128 / 64 / 32 / 16 / 8 / 4 / 2 / 1
1 / 1 / 0 / 0 / 1 / 0 / 1 / 0

Gives: 128 + 64 +8 +2

Answer: 202

Your turn:

Work through these and then share your answers with your shoulder partner – discuss any differences in your answers.

Convert the denary (base 10) numbers to binary (base 2) and then convert them back again to check your answers. Use both methods to see which you find the easiest to use.

A)  175

Answer:

Convert back to denary by adding up the columns with 1 in (show your working):

B)  240

Answer:

Convert back to denary by adding up the columns with 1 in (show your working):