Convert Decimal to Binary

How do you convert the following decimal number to binary? 25

Technique 1 Ladder Technique

Step 1: Divide the number by 2. Store the remainder. This remainder is the first digit of your new binary number.

Step 2: Divide the quotient from previous division by 2. Store the remainder. This remainder is the second digit of your new binary number.

Step 3: Repeat this process until quotient equals 0.

Step 3: Repeat this process until quotient equals 0.

Step 3: Repeat this process until quotient equals 0.

Step 4: Answer reads down. Therefore the decimal 25 is equal to 11001 in binary.

This technique works when you want to convert from decimal to any other base. You simply divide by the base you are converting to. Example: convert decimal 25 to hex. 16 1 1 16 25 9 decimal 25 = 19 in hex (can be written as 2510 = 1916 )

Technique 2 Positional Notation

How do you convert the following decimal number to binary using positional notation? 25

Step 1: Create a positional chart for binary. 64 32 16 8 4 2 1 26 25 24 23 22 21 20

16 + 8 + 1 = 25 Step 2: Select place values that when added together equal 25. 64 32 16 8 4 2 1 26 25 24 23 22 21 20 16 + 8 + 1 = 25

Step 3: Write a binary digit 1 for all selected place values. Write a 0 for all place values not selected. 64 32 16 8 4 2 1 26 25 24 23 22 21 20 2510 = 110012

32 + 16 + 4 + 1 = 53 5310 = 1101012 Another Example: 5310 = _______ 2 64 32 16 8 4 2 1 26 25 24 23 22 21 20 32 + 16 + 4 + 1 = 53 5310 = 1101012