Answer :
To convert the binary number [tex]\( 11001_2 \)[/tex] to its decimal (base ten) equivalent, we will use the method of expanding the binary number using powers of 2. Let's break down the steps:
1. Identify the positions and powers of 2:
Each digit in the binary number represents an increasing power of 2, starting from the right-hand side at position 0.
The binary number [tex]\( 11001_2 \)[/tex] has the digits, from left to right, at the following positions:
[tex]\[ 1 \cdot 2^4, 1 \cdot 2^3, 0 \cdot 2^2, 0 \cdot 2^1, 1 \cdot 2^0 \][/tex]
2. Calculate the value of each digit:
- The leftmost digit (1) is in position 4:
[tex]\[ 1 \times 2^4 = 1 \times 16 = 16 \][/tex]
- The next digit (1) is in position 3:
[tex]\[ 1 \times 2^3 = 1 \times 8 = 8 \][/tex]
- The middle digit (0) is in position 2:
[tex]\[ 0 \times 2^2 = 0 \times 4 = 0 \][/tex]
- The next digit (0) is in position 1:
[tex]\[ 0 \times 2^1 = 0 \times 2 = 0 \][/tex]
- The rightmost digit (1) is in position 0:
[tex]\[ 1 \times 2^0 = 1 \times 1 = 1 \][/tex]
3. Sum all these values together:
[tex]\[ 16 + 8 + 0 + 0 + 1 = 25 \][/tex]
Therefore, [tex]\( 11001_2 \)[/tex] written in base ten is 25.
So, the correct answer is:
b. 25
1. Identify the positions and powers of 2:
Each digit in the binary number represents an increasing power of 2, starting from the right-hand side at position 0.
The binary number [tex]\( 11001_2 \)[/tex] has the digits, from left to right, at the following positions:
[tex]\[ 1 \cdot 2^4, 1 \cdot 2^3, 0 \cdot 2^2, 0 \cdot 2^1, 1 \cdot 2^0 \][/tex]
2. Calculate the value of each digit:
- The leftmost digit (1) is in position 4:
[tex]\[ 1 \times 2^4 = 1 \times 16 = 16 \][/tex]
- The next digit (1) is in position 3:
[tex]\[ 1 \times 2^3 = 1 \times 8 = 8 \][/tex]
- The middle digit (0) is in position 2:
[tex]\[ 0 \times 2^2 = 0 \times 4 = 0 \][/tex]
- The next digit (0) is in position 1:
[tex]\[ 0 \times 2^1 = 0 \times 2 = 0 \][/tex]
- The rightmost digit (1) is in position 0:
[tex]\[ 1 \times 2^0 = 1 \times 1 = 1 \][/tex]
3. Sum all these values together:
[tex]\[ 16 + 8 + 0 + 0 + 1 = 25 \][/tex]
Therefore, [tex]\( 11001_2 \)[/tex] written in base ten is 25.
So, the correct answer is:
b. 25
