Binary Blast-off
BINARY BLAST OFF
Welcome to the Intergalactic Academy. Your mission is to fuel your spaceship by solving binary addition problems. Each correct calculation powers up the fuel cells. Prepare for launch!
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High Score: 0
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Highest Streak: 0
SPACESHIP FUEL
Fuel Cell Challenge
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Binary Rules
- 0 + 0 = 0
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 1 = 10 (0, carry 1)
How it works:
Binary addition
When two numbers are added together in denary (decimal), the first number is combined with the second number to produce a sum. For example, 1 + 2 = 3.
When two numbers are added together in denary (decimal), the first number is combined with the second number to produce a sum. For example, 1 + 2 = 3.
In binary addition, different rules are applied. There are four basic rules for adding two binary numbers:
Example – adding 01 + 10
1 + 0 = 1
0 + 1 = 1
Result in binary: 11 (which represents denary 3)
- 0 + 0 = 0
- 1 + 0 = 1
- 1 + 1 = 10 (binary equivalent of denary 2)
- 1 + 1 + 1 = 11 (binary equivalent of denary 3)
Example – adding 01 + 10
1 + 0 = 1
0 + 1 = 1
Result in binary: 11 (which represents denary 3)
Adding binary numbers is similar to adding denary numbers however, instead of carrying groups of ten, you carry groups of 2.
Example – adding 01 + 01
1 + 1 = 0, carry 1
0 + 0 + 1 = 1
Result in binary: 10 (which represents denary 2)
Example – adding 01 + 01
1 + 1 = 0, carry 1
0 + 0 + 1 = 1
Result in binary: 10 (which represents denary 2)
Note: When we add two 1s we need to carry over to the next column.
Checking your answer
You can check your answers by converting each binary number into denary (decimal) and checking the calculation.
Example:
1101 (binary) = 13 (denary)
0101 (binary) = 5 (denary)
Binary addition: 1101 + 0101 = 10010
Denary check: 13 + 5 = 18. The binary result 10010 is also 18.
Checking your answer
You can check your answers by converting each binary number into denary (decimal) and checking the calculation.
Example:
1101 (binary) = 13 (denary)
0101 (binary) = 5 (denary)
Binary addition: 1101 + 0101 = 10010
Denary check: 13 + 5 = 18. The binary result 10010 is also 18.
Overflow
Overflow errors occur when a calculation produces a result that exceeds the bit limit of the system. Using four bits, the largest value possible is 1111 (denary 15). When adding two four-bit numbers, the result may require more than four bits. For instance, adding 1011 (denary 11) and 1100 (denary 12) will result in the following:
Overflow errors occur when a calculation produces a result that exceeds the bit limit of the system. Using four bits, the largest value possible is 1111 (denary 15). When adding two four-bit numbers, the result may require more than four bits. For instance, adding 1011 (denary 11) and 1100 (denary 12) will result in the following:
The actual sum is 10111 (denary 23), which needs five bits. However, if only four bits are available, the result would be 0111 (denary 7). Overflow can affect the accuracy of calculations.
You may also be interested in:
- Binary Brainiac game
- Binary Blitz! game
- Binary Blaster game
- Binary Flip game
- Binary Calculator
Tags: Games, computing games