the binary system is used for computer programming. a binary number consists of a string of digits that are either 0s or 1s

a. if a string of binary code is 5 digits long, how many binary numbers are possible if the first digit is a 1?
b. how many different binary numbers can be represented by a string of binary code with 5 digits if the first digit is 1 and the last two digits are 0?

The maximum binary numbers ocur when

all 5 digits are 1s: 1 1 1 1 1 base 2.

a. 5 binary numbers are possible.

b. 1 1 1 0 0 base 2.

1*2^4, 1*2^3, and 1*2^2 =
16, 8, and 4 = 3 binary numbers that can be represented.

To answer these questions, we need to understand how the binary system works. In the binary system, each digit can either be 0 or 1, and each digit represents a power of 2 starting from the right-most digit. For example, in a 5-digit binary number, the right-most digit represents 2^0, the next digit represents 2^1, and so on.

a. If a string of binary code is 5 digits long, and the first digit is a 1, we can calculate the number of possible binary numbers by analyzing the remaining 4 digits. Since each digit can be either 0 or 1, there are 2 choices for each of the 4 remaining digits. Therefore, the total number of possible binary numbers is 2^4 = 16.

b. If the first digit is 1 and the last two digits are 0, we need to calculate the number of possible combinations for the remaining 2 middle digits. Similar to the previous question, each of the 2 middle digits can be either 0 or 1, resulting in 2 choices for each digit. Therefore, the total number of binary numbers is 2^2 = 4.

To summarize:
a. The number of possible binary numbers with a 5-digit string and the first digit as 1 is 16.
b. The number of possible binary numbers with a 5-digit string, the first digit as 1, and the last two digits as 0 is 4.