Explain how by use of the binary system positive integer numbers are stored on digital computer and explain why binary is used rather than any other base system?

Answer 1

First, the easy part- Binary is used because digital computers use rely on the extant state of transistors to complete operations. Transistors have only two states: off (0) and on (1).

Binary-Decimal conversion is fairly simple also. The key is that each order of magnitude in a binary number represents a power of two.

So starting at the least significant bit (to the far right) it is 2^0:

1=1

0=0

Next is 2^1:

1=2

0=0

2^2:

1=4

0=0

And so on. So if one had 10101101 as their integer:

2^0 = 1 = 1

2^1 = 0 = 0

2^2 = 1 = 4

2^3 = 1 = 8

2^4 = 0 = 0

2^5 = 1 = 32

2^6 = 0 = 0

2^7 = 1 = 128

The integer is the sum of each bit's value, in this case 173.