Decomposition of a number into bit terms

In this publication, we will consider what bit terms are, and how to represent a number as their sum (or decompose into them). We will also analyze examples for a better understanding of the material presented.

The sum of the bit terms

Any natural multi-digit number (it contains several digits) can be written as a sum of bit terms.

For example:

The number “47” consists of four tens and seven units.

I.e. 47 = 4 10 + 7 1 = 40 + 7

The action above is called the decomposition into bit terms (or their sum), which in this case are the numbers “40” and “7”.

examples:

• 213 = 2 hundreds + 1 tens + 3 units = 2 · 100 + 1 · 10 + 3 · 1 = + + 200 10 3
• 409 = 4 hundreds + 0 tens + 9 ones = 4 · 100 + 0 · 10 + 9 · 1 = 400 + 9
• 5 = 380 thousand + 5 hundreds + 3 tens + 8 units = 5 · 1000 + 3 · 100 + 8 · 10 + 0 · 1 = + + 5000 300 80

Multipliers 1, 10, 100, 1000, etc. – this is bit units.

Example of a problem

Let’s decompose the number 4 215 096 into bit terms and determine the number of units of each bit.

Decision:

The given number contains:

• 4 million;
• 2 hundred thousand;
• 1 ten thousand;
• 5 thousand;
• 0 hundreds;
• 9 tens;
• 6 units.

Let’s write the number as a sum of bit terms:

4 215 096 = 4 · 1 000 000 + 2 100 000 + 1 10 000 + 5 · 1000 + 0 · 100 + 9 · 10 + 6 · 1 = 4 000 000 + 200 000 + 10 000 + 5000 + 90 + 6.

In order to determine how many bit units are contained in a number, we simply rewrite it to the bit, the number of units of which we need to find. In our case, it turns out: