CONVERSION OF OTHER BASES TO DENARY SYSTEM
Conversion of other bases to denary system. To convert numbers in the other bases to denary system, expand the given number in power of its bases.
Examples:
- Convert 35416 to denary
35416 = 3 x 162 + 5 X 161 + 4 x 160
= 3 x 256 + 5 x 16 + 4 x 1
= 768 + 80 + 4
852ten
- Convert 255eight to base ten
2558 = 2 x 82 + 5 x 81 + 5 x 80
= 2 x 64 + 5 x 8 + 5 x 1
= 128 + 40 + 5
= 173ten
- Convert 10110012 to base ten
1011001two = 1 x 26 + 0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20
= 1 x 64 + 0 x 32 + 1 x 16 + 1 x 8 + 0 X 4 + 0 x 2 + 1 x 1
= 64 + 0 + 16 + 8 + 0 + 0 +1
= 89ten
- Convert 3A716 to base ten
3A716 = 3 x 162 + 10 x 161 + 7 x 160
= 3 x 256 + 10 x 16 + 7 x 1
= 768 + 160 + 7
= 935ten
ADDITION, SUBTRACTION AND MULTIPLICATION OF BINARY NUMBERS
There are four rule guiding binary addition
0 + 0 = 0
0 + 1 = 1 (Always remember you are working with binary digit not decimal)
1 + 0 = 1
1 + 1 = 10
- Add 1012 + 10002
- Add 10011012 + 1110012
- 1012
+ 10002
11012
- 10011012
+ 1110012
100001102
Binary Subtraction
0 – 0 = 0; 0 – 1 = 1; 1 – 0 = 1; 1 – 1 = 0
(1). Subtract 1012 from 10012 (2). 100012 – 11112
- 10012
– 1012
1002
- 10001
– 1111
00102
Binary Multiplication
The rules for binary multiplication are: 0 x0 = 0; 1 x 0 = 0; 0 x 1 = 0; 1 x 1 = 1
(1).11012 x 1102 (2). 1012 x 102
- 11012
x 1102
00002
+ 11012
11012
10011102
- 1012
x 102
0002
+ 1012
10102
| Decimal | Binary | Octal | Hexadecimal |
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
EVALUATION
- Define number base
- Convert the following to base 10
- 10011two
- 317eight
- Evaluate the following:
- 1012 x 1012
- 1110012 + 10012
- 101112 – 1002
See also