Sure, let's convert these hexadecimal numbers to decimal.

a. 6BF9
This is a positive number because the first digit is less than 8.

To convert it to decimal, we can use the formula for hexadecimal conversion which is:

(decimal) = (hex_digit) * (16 ^ position)

where the position is the index of the digit from right to left, starting from 0.

So, for 6BF9:

(decimal) = 9*(16^0) + 15*(16^1) + 11*(16^2) + 6*(16^3)
(decimal) = 9 + 240 + 2816 + 24576
(decimal) = 27641

b. C123
This is a negative number because the first digit is greater than 7.

To convert it to decimal, we first convert it as if it was positive, and then subtract the result from 2^16 (because we're dealing with 16-bit numbers).

So, for C123:

(decimal) = 3*(16^0) + 2*(16^1) + 1*(16^2) + 12*(16^3)
(decimal) = 3 + 32 + 256 + 49152
(decimal) = 49443

But since it's negative, we subtract this from 2^16:

(decimal) = 2^16 - 49443
(decimal) = 65536 - 49443
(decimal) = -16093

So, the decimal equivalents of the given hexadecimal numbers are:

a. 6BF9 = 27641
b. C123 = -16093

Question

Sure, let's convert these hexadecimal numbers to decimal.

a. 6BF9
This is a positive number because the first digit is less than 8.

To convert it to decimal, we can use the formula for hexadecimal conversion which is:

(decimal) = (hex_digit) * (16 ^ position)

where the position is the index of the digit from right to left, starting from 0.

So, for 6BF9:

(decimal) = 9*(16^0) + 15*(16^1) + 11*(16^2) + 6*(16^3)
(decimal) = 9 + 240 + 2816 + 24576
(decimal) = 27641

b. C123
This is a negative number because the first digit is greater than 7.

To convert it to decimal, we first convert it as if it was positive, and then subtract the result from 2^16 (because we're dealing with 16-bit numbers).

So, for C123:

(decimal) = 3*(16^0) + 2*(16^1) + 1*(16^2) + 12*(16^3)
(decimal) = 3 + 32 + 256 + 49152
(decimal) = 49443

But since it's negative, we subtract this from 2^16:

(decimal) = 2^16 - 49443
(decimal) = 65536 - 49443
(decimal) = -16093

So, the decimal equivalents of the given hexadecimal numbers are:

a. 6BF9 = 27641
b. C123 = -16093

Knowee AI · Accepted Answer