Converting Between Binary & Denary
Converting Denary to Binary Walkthrough:
- Write down the powers of 2 in binary from right to left, starting with 20 (1), 21 (2), 22 (4), 23 (8), and so on, until you reach 128 (as answers must be given in 8 bits)
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
|
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
- Starting from the leftmost column, write a 1 if the corresponding power of 2 is less than or equal to the number you’re converting, 171 in this example, otherwise write a 0.
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
|
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
- Check your working by adding together all column headings with a 1 underneath (128+32+8+2+1=171)
- Read the binary digits from left to right to get the binary equivalent of 171.
10101011
Converting Binary to Denary Walkthrough:
- Write down the powers of 2 in decimal from right to left, starting with 20 (1), 21 (2), 22 (4), 23 (8), and so on, until you reach 128 (as answers must be given in 8 bits)
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
- Starting from the leftmost column, write the binary digit in the column if it is a 1 write 1, and write 0 if it is a 0.
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
|
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
- Add up the values in each column where the binary digit is 1.
64 + 32 + 4 + 2 = 102
Exam Tip
- If the question tells you to show your working you will get a mark for this so don't forget to write down yours
