Adding Binary Numbers
You’ll need to be able to add together up to three binary numbers, and it’s really easy for AQA:
- You’ll only ever need to add up to three binary numbers using a maximum of 8 bits per number.
- Only a maximum of three 1s will be added in a single column.
- Answers will be a maximum of 8 bits in length.
- No carrying beyond the 8th bit will be involved.
Example
| Carrying |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
|
0 |
1 |
0 |
1 |
1 |
0 |
1 |
0 |
|
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
| + |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
Applying a Binary Shift
You’ll need to be able to apply a binary shift to a binary number.
Logical Left Shift
- Shifts all bits to the left, appending a 0 to the right end.
- Each left shift multiplies the number by 2.
Example
00101101 << 1 = 01011010
What happened, in decimal:
45 (multiplied by 2) = 90
Logical Right Shift
- Shifts all bits to the right, appending a 0 to the left end.