a) What is the largest positive number that can be represented in 12 bits using one’s complement? Represent the number in bits and decimal as well. Assume the first bit is the sign bit. (2 marks)
To find the largest positive number that can be represented in 12 bits using one's complement, we need to understand how one's complement works.
In one's complement representation, the leftmost bit (MSB) is the sign bit. If the sign bit is 0, it represents a positive number, and if the sign bit is 1, it represents a negative number.
To represent the largest positive number in 12 bits using one's complement, we need to set all the bits, except the sign bit, to 1.
In 12 bits, the sign bit would be the 12th bit, and the remaining 11 bits can be set to 1.
Here's the binary representation of the largest positive number in 12 bits using one's complement:
1111 1111 1101
To convert this binary representation to decimal, we need to consider the sign bit. Since the sign bit is 0, it represents a positive number.
Therefore, the largest positive number that can be represented in 12 bits using one's complement is:
Binary: 1111 1111 1101
Decimal: 4093
To find the largest positive number that can be represented in 12 bits using one's complement, we need to consider the number of bits available for the actual value.
In a 12-bit representation using one's complement, the first bit is reserved as the sign bit, leaving 11 bits for the value itself. Therefore, there will be 10 bits available to represent the actual value.
To find the maximum positive number, we need to consider that all the value bits are set to 1. Let's represent this number in bits and decimal:
Bits representation: 0111 1111 1111
Decimal representation: 2047
Therefore, the largest positive number that can be represented in 12 bits using one's complement is 2047.