Conversions

Decimal numbers are what humans use, and computers use binary. So how does one convert a decimal number to a binary number?

DECIMAL TO BINARY

When converting from decimal to binary the mathematical way is simplest. Start with the decimal number you want to convert and start dividing that number by two, keeping track of the remainder after each complete division. Every time you divide by two, you will divide evenly (0) or get a remainder of one (1). Following the pattern to the end, you will get a binary number. Write the remainders in the order they were generated from right to left and the result is the equivalent binary value.

DIVIDE


    44 / 2 = 22 remainder = 0
    22 / 2 = 11 remainder = 0
    11 / 2 =  5 remainder = 1 
     5 / 2 =  2 remainder = 1
     2 / 2 =  1 remainder = 0
     1 / 2 =  0 remainder = 1

REVERSE

The bits, in the order they were generated from right to left are 101100

Reverse the order of the remainders and you get the binary number 101100 which is 44 in decimal.

BINARY TO DECIMAL

Each binary column has a corresponding decimal value. You can add the decimal values of all columns that have a '1' in them and you will get the decimal equivalent.

 

Equivalents	COLUMNS								TOTAL
Powers of 2	27	26	25	24	23	22	21	20
Decimal	128	64	32	16	8	4	2	1
BIT VALUES	0	0	0	0	0	0	0	1	1
	0	0	0	0	0	0	1	1	3
	0	0	0	0	1	1	1	0	14
	1	0	1	0	1	1	0	0	172

 

 

<<  <  1 | 2 | 3 | 4 | 5 | 6 | 7  >  >>

 

 

---

<< BITS_N_BYTES

>>