How to convert

1. Decimal to Other Bases

Decimal to Binary (Base 2)

Steps:

1. Divide the decimal number by 2.

2. Write down the remainder.

3. Keep dividing the quotient by 2 until you reach 0.

4. Read the remainders from bottom to top.

Example: Convert 25 to binary.

25 ÷ 2 = 12, remainder = 1  

12 ÷ 2 = 6, remainder = 0  

6 ÷ 2 = 3, remainder = 0  

3 ÷ 2 = 1, remainder = 1  

1 ÷ 2 = 0, remainder = 1  

Answer: 25 = 11001

Decimal to Octal (Base 8)

Steps:

1. Divide the decimal number by 8.

2. Write down the remainder.

3. Keep dividing the quotient by 8 until you reach 0.

4. Read the remainders from bottom to top.

Example: Convert 100 to octal.

100 ÷ 8 = 12, remainder = 4  

12 ÷ 8 = 1, remainder = 4  

1 ÷ 8 = 0, remainder = 1  

Answer: 100 = 144

Decimal to Hexadecimal (Base 16)

Steps:

1. Divide the decimal number by 16.

2. Write down the remainder (if ≥10, convert to A-F).

3. Keep dividing the quotient by 16 until you reach 0.

4. Read the remainders from bottom to top.

Example: Convert 255 to hexadecimal.

255 ÷ 16 = 15, remainder = 15 (F)  

15 ÷ 16 = 0, remainder = 15 (F)

Answer: 255 = FF

2. Binary to Other Bases

Binary to Decimal

Multiply each digit by 2 raised to its position power (right to left, starting at 0).

Example: Convert 1011 to decimal.

(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)  

= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)  

= 8 + 0 + 2 + 1 = 11  

Binary to Octal

Group binary digits into sets of 3 (from right). Convert each group to octal.

Example: Convert 101101 to octal.

101 101 → (5 5)  

Answer: 101101 = 55

Binary to Hexadecimal

Group binary digits into sets of 4 (from right). Convert each group to hexadecimal.

Example: Convert 11011011 to hexadecimal.

1101 1011 → (D B)  

Answer: 11011011 = DB

3. Octal & Hexadecimal to Decimal

Octal to Decimal

Multiply each digit by 8 raised to its position power.

Example: Convert 345 to decimal.

(3 × 8²) + (4 × 8¹) + (5 × 8⁰)  

= (3 × 64) + (4 × 8) + (5 × 1)  

= 192 + 32 + 5 =229

Hexadecimal to Decimal

Multiply each digit by 16 raised to its position power.

Example: Convert 2F to decimal.

(2 × 16¹) + (15 × 16⁰)  

= (2 × 16) + (15 × 1)  

= 32 + 15 = 47