Decimal number system characteristic is the linear array of digits and also their significant placing.For example number 4324 can be represented :
4324 = 4x1000 + 3x100 + 2x10 + 4x1
Number 4 on the left is of differing significance to that of number 4 on the right.
The fundamental of the decimal number system is the availability of 10 different digits.They permit counting from 0 to 9. If counting is to excees the number 9, this constitutes acarry over to the next place digit.The significance of this place is 10, and the next carry over takes place when 99 is reached.
Example: Number 83 674 098
| 107 | 106 | 105 | 104 | 103 | 102 | 101 | 100 |
| 8 | 3 | 6 | 7 | 4 | 0 | 9 | 8 |
The signifance of the "8" on the far left is 80 000 000 = 80 million, whereas the significance of the "8" in the far right is 8. The digit on the far right is reffered to as the least significant digit, and the digit on the far left as the most significant digit.
We will now apply the structures of the decimal number system to two - digit calculation.These two values are represented in the form of digits "1" and "0".
The number system is configured as folows:
| 27=128 | 26=64 | 25=32 | 24=16 | 23=8 | 22=4 | 21=2 | 20=1 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
Up to a maximum of
28 - 1 = 256 - 1 = 255
can be calculated with eight places, which would be the number 1111 11112.
The individual places of the binary number system can adopt one of the two dogits 0 or 1. This smallest possible unit of the binary system is termed 1 bit.
In the above example , a number consisting of 8 bits, i.e. one byte, has been configured. The number considered, 110010102, assumes the decimal value 20210.
1 x 27 + 1 x 2 6 + 0 x 25 +0 x 24+1 x 23+ 0 x 22 + 1 x 21 + 0 x 20 =128 +64 +0+0+8+0+2+0 = 202
