The Octal Number System
The Octal system is in base 8. We count in Octal from 0 through 7 , which is 8 numbers. Octal numbers are 3 bit binary numbers. Therefore, 111 is the highest binary number that can be converted to Octal or 4+2+1=7. Once the binary number is converted to the octal format, the weight of each column is as follows: 1's, 8's, 64's and so forth as multiples of 8.. The number 123 in Octal is 1x64=64 + 2x8=16 + 3x1=1 or 81 decimal or base 10. An example of converting a large binary number is as follows:
Binary Number = 111011001100 , taking 3 bit numbers from right to left: 100=4, 001=1, 011=3 and 111=7 this yeilds 7314 (octal)= 7x 512 + 3x64 +1x8 +4x1 = 3584 + 192 + 8 + 4 = 3788 decimal (base 10).
Below are two tables, the first shows the octal conversion of 3 bit binary numbers and the second shows examples of octal equivalents of decimal numbers.
Octal (Base 8) Conversion from Binary
| Decimal # | Binary Number | Totals |
|---|
| ------- | 4's | 2's | 1's | ------- |
|---|
| 0 |
0 |
0 |
0 |
0+0+0=0 |
|---|
| 1 |
0 |
0 |
1 |
0+0+1=1 |
|---|
| 2 |
0 |
1 |
0 |
0+2+0=2 |
|---|
| 3 |
0 |
1 |
1 |
0+2+1=3 |
|---|
| 4 |
1 |
0 |
0 |
4+0+0=4 |
|---|
| 5 |
1 |
0 |
1 |
4+0+1=5 |
|---|
| 6 |
1 |
1 |
0 |
4+2+0=6 |
|---|
| 7 |
1 |
1 |
1 |
4+2+1=7 |
|---|
Octal Address Examples (Base 8)
| Decimal # |
64's |
8's |
1's |
Totals |
|---|
| 0 |
0 |
0 |
0 |
0+0=0 |
|---|
| 15 |
0 |
1 |
7 |
0+8+7=15 |
|---|
| 16 |
0 |
2 |
0 |
0+16+0=16 |
|---|
| 511 |
7 |
7 |
7 |
448+56+7=511 |
|---|
| 327 |
5 |
0 |
7 |
320+0+7=327 |
|---|
| 250 |
3 |
7 |
2 |
192+56+2=250 |
|---|
| 64 |
1 |
0 |
0 |
64+0+0=64 |
|---|
| 156 |
2 |
3 |
4 |
128+24+4=156 |
|---|
| 403 |
6 |
2 |
3 |
384+16+3=403 |
|---|
| 427 |
6 |
5 |
3 |
384+40+3=427 |
|---|