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CPT1 - binary digits

How do you convert binary to denary (sp?)
You'll need to become best friends with a little magic table;
16 - 8 - 4 - 2 - 1

Say for example, you where wanting to convert 11001 binary into denary, then you would simply add the binary values into the magic table like so;
16 - 8 - 4 - 2 - 1
1 - 1 - 0 - 0 - 1

And from there you would simply add up all the values which have a 1 assigned to them. So in this instance; 16+8+1 = 25 denary.

The magic table values will keep on doubling till you eventually reach around 256. You can also use the magic table to convert backwards from denary into binary, by assigning the value "1" into the table, so that the outcome equals 25.
Reply 2
Avatar for Metrobeans
Metrobeans
OP
19
What's a magic table!

I got so confused, and with the lesson being last period, I switched off!
Say you where given the binary number; 010100111 to convert into denary. All you would do is create a little "Magic Table", which is basically just the number 1 doubling from right to left. Like so;
256 128 64 32 16 8 4 2 1
Now just take your binary number from above (010100111) and place it directly underneath the table like so;

256 128 64 32 16 8 4 2 1
0 1 0 1 0 0 1 1 1

From there on you just look at your table, and wherever you see the number 1, simply add the corresponding number from the Magic Table in the above column, like so; 128 + 32 + 4 + 2 + 1 = 167 denary. Also take a look at this website too, which also details the similar process adopted above.
Reply 4
Avatar for Dez
Dez
20
Consider the decimal system that we naturally use. The "magic table" would go something like this:

10000 1000 100 10 1
5 6 8 3 5

This can be read as "5 ten-thousands, 6 thousands, 8 hundreds, 3 tens, and 5 ones". Naturally, 50000 + 6000 + 800 + 30 + 5 = 56835.

Binary is similar, except instead of using ten fingers, you're now only using one. Hence each digit can only have one of two values, 0 or 1. Any value higher than 1 will require an extra digit, just like any number higher than 9 needs in decimal format.

So, we write a "magic table" with binary values instead of decimal.

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

This can be read as "1 one-hundred and twenty-eight, 0 sixty-fours, 1 thrity-two, 1 sixteen, 0 eights, 0 fours, 1 two and 1 one". 128 + 32 + 16 + 2 + 1 = 179, which is what binary 10110011 represents.

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