Decimal to Binary

Decimal Number Definition:A decimal number is a number expressed in the base-ten numerical system. It uses ten symbols—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—to represent quantities. Each digit's position in a decimal number corresponds to a power of 10.

Decimal Number Example:The number 4567 is a decimal number. In this number, 4 is in the thousands place, 5 is in the hundreds place, 6 is in the tens place, and 7 is in the ones place.

Binary Number Definition:A binary number is a number expressed in the base-two numerical system. It uses two symbols—0 and 1—to represent quantities. Each digit's position in a binary number corresponds to a power of 2.

Binary Number Example:The binary number 10110 is an example. In this number, 1 is in the 16s place (2^4), 0 is in the 8s place (2^3), 1 is in the 4s place (2^2), 1 is in the 2s place (2^1), and 0 is in the 1s place (2^0). When converted to decimal, this binary number represents the decimal number 22.

Conversion Process: Decimal to Binary

1. Divide by 2: Begin by dividing the decimal number by 2.
2. Record Remainders: Record the remainder (either 0 or 1) after each division. These remainders will form the binary digits.
3. Repeat Division: Continue dividing the quotient by 2 until the quotient becomes 0.
4. Reverse the Remainders: Once all divisions are done, the binary digits obtained are reversed to get the final binary number.

Example: Convert Decimal 27 to Binary

Step 1: $\frac{27}{2} = 13$ Remainder 1
Step 2: $\frac{13}{2} = 6$ Remainder 1
Step 3: $\frac{6}{2} = 3$ Remainder 0
Step 4: $\frac{3}{2} = 1$ Remainder 1
Step 5: $\frac{1}{2} = 0$ Remainder 1

Reversing the remainders, we get 11011. Therefore, the binary representation of decimal number 27 is 11011.