How to Convert Binary to Decimal

Did I mention that converting Binary to Decimal is more fun? Yes, How to Convert Binary to Decimal will show you in few easy steps what Binary to Decimal conversion is all about. As you probably already noticed, I have dedicated for each Base System 2 articles to cover all conversion scenario, therefore, I highly recommend you first read Base 10 System conversion article, before going through the Binary conversion to decimal or hexadecimal steps.

Converting Binary to Decimal

Converting binary to decimal is more fun and easier than converting Decimal to Binary.

E.g. convert 10001110 binary to decimal

Step 1: write down the Binary chart, and plug the binary starting from right to left.

128  64  32  16  8  4  2  1
  1   0   0   0  1  1  1  0

Step 2: add only the ON places; remember that 1 turns ON the Place above it. 128 + 8 + 4 + 2 = 142.

Therefore, 10001110 equal to 142 Decimal.

Note: the steps will be minimized with the next examples.

Convert 101101 Binary to Decimal

Step 1: write down the binary chart, and plug the binary starting from right to left.

128  64  32  16  8  4  2  1
  0   0   1   0  1  1  0  1

Step 2: add only the ON places. 32 + 8 + 4 + 1 = 45

Always drop the Left leading Zeros when you write your answer.

Therefore, 101101 equal to 45 decimal.

Convert 10101110 to Decimal

Step 1: write down the binary chart, and plug the binary starting from right to left.

128  64  32  16  8  4  2  1
  1   0   1   0  1  1  1  0

Step 2: add only the ON places. 128 + 32 + 8 + 4 + 2 = 174

Therefore, 10101110 equal to 174 decimal.

Convert 11011001 to Decimal

Step 1: write down the binary chart, and plug the binary starting from right to left.

128  64  32  16  8  4  2  1
  1   1   0   1  1  0  0  1

Step 2: add only the ON places. 128 + 64 + 16 + 8 + 1 = 217

Therefore, 11011001 equal to 217 decimal.

Convert 1011 to Decimal

Step 1: Try to answer without the binary chart.

Step 2: write down nibble 1011 on a piece of paper and add only the ON places.

8 + 2 + 1 = 11

1011 = 11

Therefore, 1011 equal to 11 decimal.

Binary to Decimal and Hex Chart

After this practice, you should be able to know by heart all nibbles’ decimal value from 0000 (0) up to 1111 (15), and nibbles’ Hex value from 1010 (A) up to 1111 (F).

• 0 = 0000
• 1 = 0001
• 2 = 0010
• 3 = 0011
• 4 = 0100
• 5 = 0101
• 6 = 0110
• 7 = 0111
• 8 = 1000
• 9 = 1001
• 10 = 1010 = A
• 11 = 1011 = B
• 12 = 1100 = C
• 13 = 1101 = D
  
• 14 = 1110 = E
• 15 = 1111 = F

Subject Related

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