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How to Count in Binary Numbers
August 1, 2024

#### Introduction

This blog describes how to count in binary numbers and uses decimal numbers (0-9) in some examples to make the topic easier to understand. A table describes how counting in binary numbers relates to counting in decimal numbers, and demonstrates that they represent the same values.

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#### Decimal Numbers (Base 10)

The numbers you use in every day life are called “decimal” numbers, meaning they are based on the number 10. The decimal numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This set of numbers are sometimes referred to as “base 10”, meaning there are 10 individual numbers. Just as the 26 letters of the alphabet make up all possible words in the English language, so to do the numbers 0 – 9 make up all possible decimal, or base 10, numbers.

#### Counting in Decimal

Counting in decimal proceeds through the digits 0 – 9,

(1)

A second digit is needed to represent more numbers. Since there are only ten total numbers, its necessary to start combining some of the digits 0 – 9 together to build larger numbers. The next number is created by adding a 1 digit and counting to repeat the sequence 0 – 9 in the second digit,

(2)

Again, its necessary to combine the set of numbers to make larger numbers. The first digit is incremented from 1 to 2, and then the second digit again repeats 0 – 9,

(3)

This pattern repeats until we reach 99,

(4)

A 1 digit is prepended to create an even larger number and the other digits roll-over back to 0,

(5)

#### Binary Numbers (Base 2)

Binary numbers are made up of two digits: 0 and 1, which is why binary math is sometimes referred to as “base 2”. The digits 0 and 1 make up all possible base 2 numbers, just as the digits 0 – 9 make up all possible base 10 numbers.

#### Counting in Binary

Counting in decimal proceeds through the digits 0 – 1,

(6)

Now a second digit is needed to represent more base 2 numbers. The 1 digit is prepended to create more numbers,

(7)

Another 1 is prepended to create even more numbers,

(8)

This process continues to repeat,

(9)

and then

(10)

By convention, a 0 digit can be prepended to a binary number with no change in value. For example, binary 1 and binary 01 are the same value. Similarly, binary 11 and 011 are the same value. Any number of zeros can be added to the front of a number with no change in value, such that 1101 is equivalent to 000001101.

Counting up to 4 digits could be represented by:

(11)

#### Comparing Binary to Decimal

Because there are less numbers in base 2 than base 10, the number of digits in base 2 numbers grows more rapidly than base 10, although they still represent the same value. The following table presents the equivalent base 2 number to the base 10 number.

(12)

#### Conclusion

This blog described how to count in binary numbers, base 2, and decimal numbers (0-9) with provided examples. A table was used to compare the binary and decimal values, showing how the two number formats still represent the same values although with different digits.

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Behold, I am toward God as you are; I too was pinched off from a piece of clay. Job 33:6
Enter His gates with thanksgiving, and His courts with praise! Give thanks to Him; bless His name! Psalm 100:4
Lift up your hands to the holy place and bless the Lord! Psalm 134:2
Blessed is the man who trusts in the Lord, whose trust is the Lord. He is like a tree planted by water, that sends out its roots by the stream, and does not fear when heat comes, for its leaves remain green, and is not anxious in the year of drought, for it does not cease to bear fruit. Jeremiah 17:7-8
He said to him, “You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself. On these two commandments depend all the Law and the Prophets.” Matthew 22:37-39
Then He said to me, “Prophesy over these bones, and say to them, O dry bones, hear the word of the Lord. Thus says the Lord God to these bones: Behold, I will cause breath to enter you, and you shall live." Ezekiel 37:4-5
Riches do not profit in the day of wrath, but righteousness delivers from death. Proverbs 11:4
The angel of the Lord appeared to him in a flame of fire out of the midst of a bush. He looked, and behold, the bush was burning, yet it was not consumed. And Moses said, “I will turn aside to see this great sight, why the bush is not burned.” When the Lord saw that he turned aside to see, God called to him out of the bush, “Moses, Moses!” And he said, “Here I am.” Exodus 3:2-3
Daniel answered and said: “Blessed be the name of God forever and ever, to whom belong wisdom and might. He changes times and seasons; He removes kings and sets up kings; He gives wisdom to the wise and knowledge to those who have understanding." Daniel 2:20-21
Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom. 2 Corinthians 3:17

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