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Binary and Logic Lesson 4 - Binary Addition

Last updated 10 months ago
16 questions

Learning Objectives

1: Understand the binary system
2: Know how to convert Denary to Binary


For revision, use the BBC Bitesize link: https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/1

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.
1

What is Binary?

How to convert add binary numbers

https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/4


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

--------------------------------------------------------------
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)
----------------------------------------------------------------


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
-----------------------------------------------
1 1 0 1 0 1 1 0
---------------------------------------------
Carry 1 1 1
1

0 + 0 =

1

0 + 1 =

1

1 + 0 =

1

1 + 1 =

1

1 + 1 + 1 =

1

What is
0111 +
0100

1

What is 1011 in Denary?

1

What is
0011 +
0010

1

What is
0011 +
0011

1

What is
0110 +
0110

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.

https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/5
1

What is it called when you have a binary number that is too large to store?

1

What is
1111 +
0001

Circle the overflow error

1

What is
0111 +
0111

Circle the overflow error

1

Challenge:
What is
1111 +
1010 +
1001

Circle the overflow error.

Hint: Check your answer by turning the binary numbers into denary.

0

Go onto this link: https://learncomputing.org/binary#


Click on "Choose Quiz"
Click "GCSE"
then choose "Binary Addition"

Screenshot your progress.