Denary to Binary
Step by step guide for year 7
What is binary
Binary is how computers store and represent data. In the computer there are loads of switches with only 2 states on or off. These are represented by ones and zeros. One is on and zero is off.
What is denary
Denary is a base 10 number system. 256 is a Denary number because it has 6-1, 5-10 and 2-100
which= 256.
Binary data
Converting Denary to Binary
Binary numbers are a base 2 numbering system and the decimal places start at 1 and multiply by 2 from right to left e.g 1,2,4,8,16,32,64,128 e.t.c.
Denary numbers are base 10 and the decimal places start at 1 and multiply 10 from right to left e.g 1,10,100,1000
For example to covert 139 to binary you need to ask:
- is 139=>128 yes it is so put a 1 and subtract 128 from 139 giving you 11
- is 11=>64 no it isn't so put a 0 and go to the next number
- is 11=>32 no it isn't so put a 0 and go on to the next number
- is 11=>16 no it isn't so put a 0 and go on to the next number
- is 11=>8 yes it is so put a 1 and subtract subtract 8 from 11 which is 3
- is 3=>4 no it isn't so put a 0 and go on to the next number
- is 3=>2 yes so put a 1 and subtract 2 from 3 that gives you 1
- is 1=>1 yes so put a 1 and subtract 1 from 1 giving you 0
Converting Binary to Denary
To find the Denary number you have to add all base 2 numbers which are represented as 1.
If the Binary code is 10101010 it is.
128+0+32+0+8+0+2+1=170
so the Denary number is 170
Adding 2 Binary numbers together
Rules: there are rules for this that:
0+1=1 1+0=1 1+1=10 1 1+1=11
10001001+10001001