Question

What is the value of the decimal number -3 using 3 bit binary representation in excess 4? Your answer should be in binary number.

Answer 1

The decimal number -3 is represented as 001 in a 3-bit binary format using the excess-4 method, where you first add the excess amount, which is 4, to the number and then convert the sum to binary.

Step-by-step explanation:

The student is asking about representing the decimal number -3 in a 3-bit binary format using the excess-4 method. Excess-4 is a way of encoding numbers such that the number is represented by its value plus 4 (the excess amount). This method allows both positive and negative numbers to be expressed in binary form without requiring a sign bit. With 3 bits, the maximum number we can encode using excess-4 is 3 (since 7-4=3), and the minimum is -4 (since 0-4=-4).

Here are the steps to represent -3 in excess-4:

1. Add 4 (the excess) to the number: -3 + 4 = 1.
2. Convert the resulting sum to binary: 1 in binary is 001.

The 3-bit binary representation of the number -3 using excess-4 encoding is 001.