Learn Binary Number System-2

Continued from Last Week's Post

This is the continuation of last week's article, Learn the Binary Number System 

Last week, we went through the fundamentals of the Binary Number System, learned how to convert the decimal number 10 to binary, and used different ways to convert a decimal number to Binary.

I hope you have tried converting the sample number 255 yourself. 

If you could not do it, then let us try it here.

Method-1:

1. Find the highest integer value in the binary table that can be subtracted from the Decimal Number. Here, 128 is the highest value that can be taken.

255

-128

=127

2. Write the binary digit 1 at the 128 (2⁷) number position underneath the Binary Table.

215	214	213	212	211	210	29	28	27	26	25	24	23	22	21	20
32,768	16,384	8,192	4,096	2,048	1,024	512	256	128	64	32	16	8	4	2	1
								1

3. The next highest integer in the binary Table that goes into 127 is 64.

127

-64

=63

215	214	213	212	211	210	29	28	27	26	25	24	23	22	21	20
32,768	16,384	8,192	4,096	2,048	1,024	512	256	128	64	32	16	8	4	2	1
								1	1

4. Repeat this method up to the unit Value position.

215	214	213	212	211	210	29	28	27	26	25	24	23	22	21	20
32,768	16,384	8,192	4,096	2,048	1,024	512	256	128	64	32	16	8	4	2	1
								1	1	1	1	1	1	1	1

You can cross-check the result by adding up all values taken from the 1s bit (the name of the binary digit) position to arrive at the total value you were trying to convert into Binary.

Method-2:

1. Divide the decimal number by 2, take the remainder, and write it at the unit position in the Binary Table.

   255/2 = Quotient = 127, Remainder = 1

2. Next step, take the Quotient Value (127) of the previous calculation, divide it by 2, and find the remainder. Write the remainder value to the left of the earlier written binary digit (bit).  Repeat this method and write the final remainder in the binary table.

127/2 = Quotient = 63,  Remainder = 1

63/2   =  Quotient = 31,  Remainder = 1

31/2   =  Quotient = 15,  Remainder = 1

15/2   =  Quotient =   7,  Remainder = 1

7/2   =  Quotient =     3,  Remainder = 1

3/2   =  Quotient =     1,  Remainder = 1

1/2   =  Quotient =     0,  Remainder = 1

You will get the Binary Number 11111111 equal the Decimal Number 255.

You can experiment with larger decimal values or write some unknown Binary Values with random 1s and 0s and try converting them back into Decimal Numbers.

Next, let us try some additions and subtractions with Binary Numbers.  If you know the rules of Decimal addition and subtraction, then you have no problems with Binary Numbers. 

Example: Addition

11101110	238
+1110111	119
101100101	357

Start adding the rightmost digits:

1.   0+1 = 1

2.   Next 1+1 = 2, put 0 and carry 2 to the next position (like 5+5=10, we put 0 at the unit's position and carry 1 to the next position to add)

3.   next 1+1+1 carry = 3 (binary 11), put 1 and carry 2 to the next position

4.   next 1+1 carry = 2(binary 10), put 0 and carry 2 to the next position

5.   Next 1+1 carry = 2(binary 10), put 0 and carry 2 to the next position

6.   Next 1+1+1 carry = 3(binary 11), put 1 and carry 2 to the next position

7.   Next 1+1+1 carry = 3(binary 11), put 1 and carry 2 to the next position

8.   Next 1+1 carry = 2(binary 10), put 0 and carry 2 to the next position.

Example: Subtraction

11001110	206
-1111111	127
1001111	79

1.   0-1 cannot be done, so take 2 from the next position; now 2-1 = 1, but the next position on the first line becomes 0.

2.   0-1 cannot be done, so take 2 from the next position; now 2-1 = 1, but the next position on the first line becomes 0.

3.   0-1 cannot be done, so take 2 from the next position; now 2-1 = 1, and the next 3 positions become 0.

4.   Take the value from the 8th position and move forward to the 4 positions and to the 2 value position; 2-1 = 1

5.   1-1 = 0

6.   1-1 = 0

7.    After moving the value forward from the 7th digit position on the top line, it is now 0.  So move 2 from the next position. 2-1 = 1

You can try it out yourself, starting with smaller binary values and progressively with bigger ones.

For your information, there is no Multiplication or Division in computers.  These calculations are achieved by successive addition or subtraction of values.

Continued../-

Earlier Post Link References:

1. Learn the Binary Numbering System
2. Learn Binary Numbering System-2
3. Octal Numbering System
4. Hexadecimal Numbering System
5. Colors 24-Bits And Binary Conversion.
6. Create Your Own Color Palette