Conversion of Binary Numbers to Base 10 Model20250123001

CONVERT THE FOLLOWING BINARY NUMBERS TO BASE 10

1. 110110
2. 11011
3. 101011
4. 011011011

Binary to Decimal Conversion

1. Convert \(110110_2\) to Base 10

Step 1: Write down the binary number and its positional values:
\[ 110110_2 = 1 \cdot 2^5 + 1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 \]

Step 2: Calculate each term:
\[ = 1 \cdot 32 + 1 \cdot 16 + 0 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 0 \cdot 1 \] \[ = 32 + 16 + 0 + 4 + 2 + 0 = 54 \]

Final Result: \(110110_2 = 54_{10}\)

2. Convert \(11011_2\) to Base 10

Step 1: Write down the binary number and its positional values:
\[ 11011_2 = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]

Step 2: Calculate each term:
\[ = 1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \] \[ = 16 + 8 + 0 + 2 + 1 = 27 \]

Final Result: \(11011_2 = 27_{10}\)

3. Convert \(101011_2\) to Base 10

Step 1: Write down the binary number and its positional values:
\[ 101011_2 = 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]

Step 2: Calculate each term:
\[ = 1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \] \[ = 32 + 0 + 8 + 0 + 2 + 1 = 43 \]

Final Result: \(101011_2 = 43_{10}\)

4. Convert \(011011011_2\) to Base 10

Step 1: Write down the binary number and its positional values:
\[ 011011011_2 = 0 \cdot 2^8 + 1 \cdot 2^7 + 1 \cdot 2^6 + 0 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]

Step 2: Calculate each term:
\[ = 0 \cdot 256 + 1 \cdot 128 + 1 \cdot 64 + 0 \cdot 32 + 1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \] \[ = 0 + 128 + 64 + 0 + 16 + 8 + 0 + 2 + 1 = 219 \]

Final Result: \(011011011_2 = 219_{10}\)

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