Converting from binary to denary

Understanding denary

People use the denary (or decimal) number system in their day-to-day lives. This system has 10 digits that we can use: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The value of each place value is calculated by multiplying by 10 (ie by the power of 10). The first few place values look like this:

ThousandsHundredsTensUnits
(1000s)(100s)(10s)(1s)

Working out the value of 1024

Thousands (1000s)Hundreds (100s)Tens (10s)Units (1s)
1024
1 × 1000 +0 × 100 +2 × 10 +4 × 1

Converting from binary to denary

To convert a binary number to denary, start by writing out the binary place values. In denary, the place values are 1, 10, 100, 1000, etc – each place value is 10 times bigger than the last. In binary, each place value is 2 times bigger than the last (ie increased by the power of 2). The first few binary place values look like this:

1286432168421

Working out the value of 1010 1000:

1286432168421
10101000
1×128 +0×64 +1×32 +0×16 +1×8 +0×4 +0×2 +0×1
128 +0 +32 + 0 +8 +0 +0 +0

So 1010 1000 in binary is equal to 168 in denary.

Machine converting binary number 10101000 into denary number 168