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Conversion of Binary Numbers to Base 10 Model20250123001

Elimu Assistant Team By Elimu Assistant Team No Comments ##binaryequations

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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