Question

Construct a table for 7-3-2-1 weighted code and represent 5698 using this code

Answer 1

The 7-3-2-1 weighted code is a binary code that assigns weightage to each bit position based on its significance. To represent 5698 using this code, convert 5698 to binary and assign weights to the bits.

Step-by-step explanation:

The 7-3-2-1 weighted code is a binary code that assigns weightage to each bit position, with the highest weight assigned to the most significant bit.

To construct a table for the 7-3-2-1 weighted code, we start with the binary representation of decimal numbers from 0 to 15 and assign weights according to the 7-3-2-1 pattern. For example, the binary representation of 0 is 0000, and the weights assigned to the bits from left to right are 7, 3, 2, and 1. The table will have two columns - one for the binary representation and another for the equivalent decimal number.

To represent 5698 using the 7-3-2-1 weighted code, we convert 5698 to binary, assign weights to the bits, and write down the code accordingly. Here's how:

1. Convert 5698 to binary: 569810 = 10110000100102

2. Assign weights to the bits: 1 (7-weight), 0 (3-weight), 1 (2-weight), 1 (1-weight), 0 (7-weight), 0 (3-weight), 0 (2-weight), 1 (1-weight), 0 (7-weight), 0 (3-weight), 1 (2-weight), 0 (1-weight), 1 (7-weight), 0 (3-weight), 0 (2-weight), 0 (1-weight)

3. Write down the code: 1011 0000 1001 0

Answer 2

The 7-3-2-1 weighted code assigns weights of 7, 3, 2, and 1 to the four digits of a binary number. To represent 5698 in this code, the binary equivalent is 1011001001011, and the corresponding 7-3-2-1 weighted code is 14124131012.

Step-by-step explanation:

The 7-3-2-1 weighted code is a binary-to-weighted code conversion system where each bit's position is assigned a specific weight. In this system, the leftmost bit has a weight of 7, the next bit has a weight of 3, followed by 2 and 1 for the subsequent bits.

To represent the decimal number 5698 in this code, we first convert it to binary. The binary representation of 5698 is 1011001001011. Now, applying the weights, we multiply each bit by its corresponding weight and sum the results. For example:

`\[ (1 * 7) + (0 * 3) + (1 * 2) + (1 * 1) + (0 * 7) + (0 * 3) + (1 * 2) + (0 * 1) + (0 * 7) + (1 * 3) + (0 * 2) + (1 * 1) = 14124131012. \]`

Therefore, the 7-3-2-1 weighted code for the decimal number 5698 is 14124131012.

In summary, the 7-3-2-1 weighted code provides a weighted representation of binary numbers, and by applying the weights to the binary equivalent of 5698, we obtain the specific code 14124131012.