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Binary Number, this is one from many theory of number. Whether it be from math class or computer science class, eventually we will need to learn about number systems, and the mathematics that is involved. But, if we learn about main system of computer, the binary number is involved too. Waht is Binary Number?


Binary numbers, as with decimal, octal, and hexadecimal numbers, are organized into columns. To learn binary math, we first need to understand how number systems operate. Let's take a look at the decimal system first, since it is simple and easier to think about. We can consider the number "1234" as,

Thousands

Hundreds

Tens

Ones

1

2

3

4



Which means,
1234 = 1x1000 + 2x100 + 3x10 + 4x1

Given,

1000 = 10^3 = 10x10x10
100 = 10^2 = 10x10
10 = 10^1 = 10
1 = 10^0 (any number to the exponent zero is one, except for zero)

The table above can be represented as,

Thousands

Hundreds

Tens

Ones

10^3

10^2

10^1

10^0

1

2

3

4



such that,

1234 = 1x1000 + 2x100 + 3x10 + 4x1 = 1x10^3 + 2x10^2 + 3x10^1 + 4x10^0

The decimal system, as with decimal math, operates in "base 10" (dec being the Latin prefix for ten) using the digits 0-9 to represent numbers, whereas the binary system, as well as its math, operates in "base 2" (bi being the Latin prefix for two) using the digits 0-1 to represent numbers. The base is also known as the radix. In other words, the table above can be represented as,

Thousands

Hundreds

Tens

Ones

Decimal

10^3

10^2

10^1

10^0

Binary

2^3

2^2

2^1

2^0



In base 10, we put the digits 0-9 in columns 10^0, 10^1, 10^2, and so on. To put a number that is greater than 9 into 10^n, we must add to 10^(n+1). For example, adding 10 to column 10^0 requires us to add 1 to the column 10^1.

In base 2, we put the digits 0-1 in columns 2^0, 2^1, 2^3, and so on. To put a number that is greater than 1 into 2^n, we must add to 2^(n+1). For example, adding 3 to column 2^0 requires us to add 1 to the column 2^1.

Here are some decimal numbers represented in binary.

Decimal

Binary

1

1

2

10

3

11

4

100

5

101

6

110

7

111

8

1000

9

1001

10

1010



5 Responses to "Binary Number, Betwen Math and Computer Science"

  1. David (July) Khoirul Says:

    Bro, terimakasih atas kunjunganny. Saya numpang tanya, apakah pendaftaran google adsense itu uda ditutup?? Saya berkali-kali daftar tapi tidak pernah diterima padahal blog saya sudah menggunakan bahasa inggris

  2. Agus Setiawan Says:

    @ David : Saya koq kurang tahu ya.... tp baru aja tgl 17 kemarin saya menambahkan Google ads baru koq masih bisa ya.

  3. faizz Says:

    waduh, msih ngantuk eehh..gak mudeng bacanya, huaaaaaaaaaaaaaaaaa...nguap mode on

  4. ariesvio Says:

    Wah...Tambah Ilmunya...Pak...Lama Tak Biner

  5. Anonymous Says:

    hi,,i just want to share link talking about binary number

    http://www.math-worksheets.co.uk/141-tmd-what-are-binary-numbers-part-1/

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