Understanding Decimal to Binary Conversion

Converting a number from the decimal system (base 10) to the binary system (base 2) is a fundamental concept in computer science and mathematics. The binary system uses only two digits, 0 and 1, to represent all numbers. To convert a decimal number to its binary equivalent, we typically use the method of repeated division by 2.

Step-by-Step Conversion of 73 to Binary

The process involves repeatedly dividing the decimal number by 2 and recording the remainder at each step. We continue this process until the quotient becomes 0. The binary representation is then obtained by reading the remainders from bottom to top.

Calculation Steps for Decimal 73

Reading the remainders from bottom to top, we get the binary representation of 73.

The remainders are: 1, 0, 0, 1, 0, 0, 1.

So, the binary representation of decimal 73 is 1001001.

Comparing with Options

Let's compare our calculated binary representation of 73 with the given options:

• Option 1: 1001100
• Option 2: 1001101
• Option 3: 1001111
• Option 4: 1001001

Our calculated value, 1001001, matches Option 4.

Revision Table: Number System Concepts

Additional Information: Positional Notation in Binary

The value of each digit in a binary number is determined by its position, just like in the decimal system. However, in binary, the positions represent powers of 2, starting from $2^0$ for the rightmost digit, then $2^1$, $2^2$, and so on, moving to the left.

Let's verify our binary number 1001001 by converting it back to decimal:

The binary number 1001001 has 7 digits. The positional values from right to left are $2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6$.

Value = (Digit at position $n$) $\times$ ($2^n$)

$1001001_2 = (1 \times 2^6) + (0 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (1 \times 2^0)$

$= (1 \times 64) + (0 \times 32) + (0 \times 16) + (1 \times 8) + (0 \times 4) + (0 \times 2) + (1 \times 1)$

$= 64 + 0 + 0 + 8 + 0 + 0 + 1$

$= 73$

This confirms that the binary representation 1001001 is indeed equivalent to the decimal number 73.