Page 84 - Electrician - TT (Volume 2)

ELECTRICIAN - CITS

Any binary number can be converted into decimal number by the above said positional weightage method.
Decimal to Binary conversion
Divide the given decimal number by 2 as shown below and note down the remainder till you get the quotient - zero.

Example
0
2 1 1 → MSB
2 2 0
2 4 0

2 8 0
2 17 1
→ LSB
2 34 0

The remainder generated by each division form the binary number. The first remainder becomes the LSB and the
last remainder becomes the MSB of binary number.

Therefore, [34] = [100010] 2
10
Counting binary number

To understand how to count with binary numbers, let us see how an odometer (Km indicator of a car) counts with
decimal numbers,

The odometer of a new car starts with the reading 0000.

After traveling 1Km , reading becomes 0001.
Successive Km produces 0002, 0003 and so on upto 0009

At the end of 10th Km , the units wheel turns back from 9 to 0, a tab on this wheel forces the tens wheel to
advance by 1. That is why the number changed from 0009 to 0010. That is, the units wheel is reset to 0 and sent
a carry to the tens wheel. Let us call this familiar action as reset and carry. The other wheels of odometer also
reset and carry. For instance, after covering 999Km , the odometer shows 0999.

After the next Km , the unit wheel resets and carries, the tens wheel resets and carries, the hundreds wheel resets
and carries and the thousands wheel advances by 1 to get the reading 01000.

Binary odometer

Visualize a binary odometer, a device whose wheels have only two digits 0 and 1. When each wheel turns, it
displays 0 then 1 and then back to 0 and the cycle repeats. A four digit binary odometer starts with 0000.

After 1km, it indicates - 0001.
The next km forces the units wheel to reset and sends carry. So the number changes to 0010.

The third km results in 0011.

After 4km, the units wheel resets and sends carry, the second wheel resets and sends carry and the third wheel
advances by 1. Hence it indicates 0100.

Table below shows all the binary numbers from 0000 to 1111 equivalent to decimal 0 to 15.

71

CITS : Power - Electrician & Wireman - Lesson 60-69