Answer :
To convert the decimal number 8 into its binary form (base two), follow these steps:
1. Identify the largest power of 2 less than or equal to the given number (8 in this case):
- \(2^3 = 8\)
2. Determine the coefficients (0s and 1s) for the powers of 2:
- Start with the highest power that fits into the given number, which is \(2^3\) in this case:
[tex]\[ 8 = 1 \cdot 2^3 \][/tex]
3. Write out the value using binary digits:
- \(2^3\) is the highest power of 2 for 8, and it fits into 8 exactly, which implies that the coefficient for \(2^3\) is 1.
- Therefore, we proceed down to the next lowest powers of 2, which are \(2^2, 2^1,\) and \(2^0\). Since \(2^3\) already accounts for the number 8 with no remainder, the coefficients for \(2^2, 2^1,\) and \(2^0\) are all 0.
Putting together these coefficients, we get:
[tex]\[ 8 = 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0 \][/tex]
4. Combine the coefficients to write the binary number:
- Therefore, 8 in binary (base two) is expressed as:
[tex]\[ 8 = \mathbf{1000}_2 \][/tex]
So, the decimal number 8 written in base two is:
[tex]\[ 8 = \boxed{1000_2} \][/tex]
1. Identify the largest power of 2 less than or equal to the given number (8 in this case):
- \(2^3 = 8\)
2. Determine the coefficients (0s and 1s) for the powers of 2:
- Start with the highest power that fits into the given number, which is \(2^3\) in this case:
[tex]\[ 8 = 1 \cdot 2^3 \][/tex]
3. Write out the value using binary digits:
- \(2^3\) is the highest power of 2 for 8, and it fits into 8 exactly, which implies that the coefficient for \(2^3\) is 1.
- Therefore, we proceed down to the next lowest powers of 2, which are \(2^2, 2^1,\) and \(2^0\). Since \(2^3\) already accounts for the number 8 with no remainder, the coefficients for \(2^2, 2^1,\) and \(2^0\) are all 0.
Putting together these coefficients, we get:
[tex]\[ 8 = 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 0 \cdot 2^0 \][/tex]
4. Combine the coefficients to write the binary number:
- Therefore, 8 in binary (base two) is expressed as:
[tex]\[ 8 = \mathbf{1000}_2 \][/tex]
So, the decimal number 8 written in base two is:
[tex]\[ 8 = \boxed{1000_2} \][/tex]
