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):
Method 1 – divide by 2, remainder 1 or 0
Method 2 – use binary columns and take it away
Convert denary number 202 into binary:
Convert denary 202 into binary:
202
101
50
25
12
6
3
1
/2
/2
/2
/2
/2
/2
/2
/2
101
50
25
12
6
3
1
0
Remainder
Remainder
Remainder
Remainder
Remainder
Remainder
Remainder
Remainder
0
1
0
1
0
0
1
1
202
128
1
32
0
16
0
10
8
1
Answer:
11001010
11001010
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
1
Gives:
Answer:
64
1
128 + 64
202
4
0
2
2
1
1
0
Search for the largest binary column heading we
can subtract from the number, take it away and
repeat with the remainder until we get an answer
of 0
Divide by 2 repeatedly noting the remainder value
each time until the answer is 0, the answer starts
at the last value
Answer:
74
64
1
32
0
16
0
8
1
+8
4
0
2
1
+2
1
0
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
Method 1 – divide by 2, remainder 1 or 0
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
Method 2 – use binary columns and take it away
128
64
32
16
8
4
2
1
Answer:
Convert back to denary by adding up the columns with 1 in (show your working):
B) 240
Method 1 – divide by 2, remainder 1 or 0
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
/2
Remainder
Method 2 – use binary columns and take it away
128
64
32
16
8
4
2
Answer:
Convert back to denary by adding up the columns with 1 in (show your working):
1