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How to convert binary to decimal

To convert a binary number (base-2) to the decimal (base-10) number system, we need to use binary place value to add the decimal value of each digit.

Each time you move a place to the left, the value increases two-fold.

1) Convert 10110 from binary to decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

16x1 + 8x0 + 4x1 + 2x1 + 1x0

= 16 + 4 + 2 = 22

So 10110 in binary is equal to 22.

2) Convert 1011011 from binary into decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

64x1 + 32x0 + 16x1 + 8x1 + 4x0 + 2x1 + 1x1

64 + 16 + 8 + 2 + 1 = 91

So 1011011 in binary is equal to 91.

How to convert decimal to binary

To convert a decimal number (base-10) to the binary (base-2) number system, we need to use rewrite the decimal number as a sum of powers of 2.

The powers of 2 are then converted to 1s in the binary place value and zeroes used as placeholders.

Example 1) Convert 13 from decimal to binary.

Step 1) Rewrite the number as a sum of powers of 2.

The powers of 2 are 1, 2, 4, 8, 16, 32, 64, ...

So 13 = 8 + 4 + 1

Or we could say that 13 = 2³ + 2² + 2⁰

Step 2) We write binary place value grid out using powers of 2 up to 2³ which is the largest.

Each power of 2 we have is represented as a one giving us:

All we need to do now is to fill in the blank numbers with zeroes.

This gives us:

So 13 = 1101 in binary.

Example 2) Convert 44 from decimal to binary.

Step 1) Rewrite the number as a sum of powers of 2.

The powers of 2 are 1, 2, 4, 8, 16, 32, 64, ...

So 44 = 32 + 8 + 4

Or we could say that 44 = 2⁵ + 2³ + 2²

Step 2) We write binary place value grid out using powers of 2 up to 2⁵ which is the largest.

Each power of 2 we have is represented as a one giving us:

All we need to do now is to fill in the blank numbers with zeroes.

This gives us:

So 44 = 101100 in binary.