Recap: What is Binary?

In computing, we often use two systems to represent numbers: binary and denary.

The binary system uses only two digits, 0 and 1 because computers only understand this.

While the denary system is the one we use every day, which includes the digits from 0 to 9.

In denary, a number is represented with Units, Tens, hundreds, thousands (Goes up by x10)

e.g. 1000 100 10 1

In binary, a number is represented with 1, 2, 4, 8, 16 .... (goes up by x2)

e.g. 128 64 32 16 8 4 2 1

Each Binary digit, is called a "bit".

E.g. The denary number 64 can be represented in binary (0s and 1s) as 01000000.

How to convert add binary numbers

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E.g. What is 01101100 + 01101010? What is the answer in Denary?

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Remember these rules:

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 10 (this is 2 in binary)

1 + 1 + 1 = 11 (this is 3 in binary)

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Step 1: Write both binary numbers on top of each other

128 64 32 16 8 4 2 1

0 1 0 0 1 1 0 0

0 1 0 0 1 0 1 0

Step 2: Start from the RIGHT side and start adding.

128 64 32 16 8 4 2 1

0 1 1 0 1 1 0 0

0 1 1 0 1 0 1 0

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1 1 0 1 0 1 1 0

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Carry 1 1 1

Binary Numbers in your computer will normally use the same amount of Bits.

E.g. 8-bits

If your binary number is too large for your computer to store, this is called an

OVERFLOW ERROR.

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