Translating binary code

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Numbers are most easily represented in binary code.

The translation from decimal digits to binary digits is done by powers of two.
Any natural number can be obtained by adding powers of two.

Here, we look at the first eight powers of two. Note that the zero power also counts.

Power	2⁰	2¹	2²	2³	2⁴	2⁵	2⁶	2⁷
Solution	1	2	4	8	16	32	64	128

To count in binary, you must order the eight first powers of two from largest to smallest.

Power	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Solution	128	64	32	16	8	4	2	1

Suppose you want to write the number 1 in binary code you must start by finding the power of two that goes with 1. That is 2⁰. So we need 1 times 2⁰. 2⁰ is on the far right, so we put a one there.

Power	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Solution	128	64	32	16	8	4	2	1
Binary number	0	0	0	0	0	0	0	1

So the binary figure 1 is 0000 0001.

Suppose you want to write the number 2 in binary code ; you must start by finding the power of two that goes with 2. That is 2¹. So we need 1 times 2¹. We put a one under 2¹.

Power	2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰
Solution	128	64	32	16	8	4	2	1
Binary number	0	0	0	0	0	0	1	0

So the binary figure 2 is 0000 0010.

Use the interaction below to experiment with this.

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