How many bits are required to represent decimal values ranging from-50 to +50?
The correct answer and explanation is :
To determine how many bits are required to represent decimal values ranging from -50 to +50, we must first understand how binary numbers work and the concept of signed numbers.
Step 1: Representing Positive Numbers
To represent the positive values, we begin by calculating how many bits are required to represent the number 50. The highest value in our range is +50, and we need to find the binary representation of 50.
First, convert 50 into binary:
50 in decimal is 110010 in binary.
Since 50 is a 6-bit number, we need at least 6 bits to represent numbers from 0 to 50.
Step 2: Adding Signed Representation (Negative Numbers)
For signed numbers (which include both positive and negative numbers), we can use a method called “two’s complement” to represent negative values. In two’s complement, one bit is reserved for the sign of the number. A 0 in the most significant bit (MSB) represents positive numbers, while a 1 in the MSB represents negative numbers.
In this case, the range of values is from -50 to +50. Since the largest magnitude in the range is 50, we need enough bits to represent the number 50 and also represent -50.
For numbers from -50 to +50, the magnitude of the values reaches 50, so we need to represent values from -50 to +50 inclusively. The binary representation of -50 in two’s complement is 11001110 for 8 bits.
Step 3: Number of Bits Required
Therefore, 8 bits are needed to represent numbers from -50 to +50 because:
- 6 bits are required to represent the positive number 50.
- An additional 1 bit is needed for the sign.
- We need 8 bits total for a signed number (including two’s complement representation).
Thus, 8 bits are required to represent decimal values ranging from -50 to +50.