Question

Convert the binary number \(1101\) into the decimal system.

Hint:

Binary to decimal conversion uses powers of 2 corresponding to each bit’s position.

Answer 1

Step 1: Write down the place values for each binary digit, starting from the rightmost digit (least significant bit). The place values are the powers of 2, increasing from right to left: \[ 2^0, 2^1, 2^2, 2^3, 2^4, \ldots \] For example, for a 5-bit binary number like \( 10101 \), the place values would be: \[ 2^4, 2^3, 2^2, 2^1, 2^0 \]
Step 2: Multiply each binary digit (bit) by its corresponding power of 2. Consider the binary number \( 10101 \): \[ 1 \times 2^4 = 16
0 \times 2^3 = 0
1 \times 2^2 = 4
0 \times 2^1 = 0
1 \times 2^0 = 1 \]
Step 3: Add all the products obtained in Step 2 to get the decimal equivalent: \[ 16 + 0 + 4 + 0 + 1 = 21 \] Therefore, the binary number \( 10101 \) is equal to \( 21 \) in decimal.