By Elimu Assistant Team 
CONVERT THE FOLLOWING BINARY NUMBERS TO BASE 10
- 110110
- 11011
- 101011
- 011011011
Binary to Decimal Conversion
1. Convert 
to Base 10
to Base 10
Step 1: Write down the binary number and its positional values:
![\[ 110110_2 = 1 \cdot 2^5 + 1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-1ae65ff2d9ec3ac691523ea09fba5484_l3.png?resize=420%2C19&ssl=1 "Rendered by QuickLaTeX.com")
Step 2: Calculate each term:
![\[ = 1 \cdot 32 + 1 \cdot 16 + 0 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 0 \cdot 1 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-fd215242d85dcbfd0ff89f646c1bbd1b_l3.png?resize=327%2C14&ssl=1 "Rendered by QuickLaTeX.com")
![\[ = 32 + 16 + 0 + 4 + 2 + 0 = 54 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-0dba87c749d4c5fa57abcba1ebafc58f_l3.png?resize=240%2C15&ssl=1 "Rendered by QuickLaTeX.com")
Final Result: 
2. Convert to Base 10
to Base 10
Step 1: Write down the binary number and its positional values:
![\[ 11011_2 = 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-51e8854d6580de1989684642d6480372_l3.png?resize=352%2C19&ssl=1 "Rendered by QuickLaTeX.com")
Step 2: Calculate each term:
![\[ = 1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-f5acc43e11b3dabad4f301d7ae4cef46_l3.png?resize=266%2C14&ssl=1 "Rendered by QuickLaTeX.com")
![\[ = 16 + 8 + 0 + 2 + 1 = 27 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-3fd66565139203e45404697b5bdaafd0_l3.png?resize=200%2C15&ssl=1 "Rendered by QuickLaTeX.com")
Final Result: 
3. Convert to Base 10
to Base 10
Step 1: Write down the binary number and its positional values:
![\[ 101011_2 = 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-0d8692fe41ee5de3bdf58c78b826212b_l3.png?resize=420%2C19&ssl=1 "Rendered by QuickLaTeX.com")
Step 2: Calculate each term:
![\[ = 1 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-63d2bde6e587f7caa22fcbcf98ad0d35_l3.png?resize=327%2C14&ssl=1 "Rendered by QuickLaTeX.com")
![\[ = 32 + 0 + 8 + 0 + 2 + 1 = 43 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-6d65580ddd84071a890fbe4cb7ca0ef5_l3.png?resize=230%2C14&ssl=1 "Rendered by QuickLaTeX.com")
Final Result: 
4. Convert to Base 10
to Base 10
Step 1: Write down the binary number and its positional values:
![\[ 011011011_2 = 0 \cdot 2^8 + 1 \cdot 2^7 + 1 \cdot 2^6 + 0 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-7cb730f0d3b603e45e5b800e837f186d_l3.png?resize=583%2C19&ssl=1 "Rendered by QuickLaTeX.com")
Step 2: Calculate each term:
![\[ = 0 \cdot 256 + 1 \cdot 128 + 1 \cdot 64 + 0 \cdot 32 + 1 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-9b4b467dfa35b231d579239c925e9184_l3.png?resize=528%2C15&ssl=1 "Rendered by QuickLaTeX.com")
![\[ = 0 + 128 + 64 + 0 + 16 + 8 + 0 + 2 + 1 = 219 \]](https://i0.wp.com/elimuassistant.co.ke/wp-content/ql-cache/quicklatex.com-5788c31b29347e10b21af783ee06d9f2_l3.png?resize=358%2C14&ssl=1 "Rendered by QuickLaTeX.com")
Final Result: 
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