# HOW TO CONVERT ANY HEX NUMBER TO DECIMAL and BINARY

Go directly to EXAMPLE CONVERSION - HEX TO BINARY

### EXAMPLE CONVERSION - HEX TO DECIMAL

Dec = decimal, Dec Equi = Decimal Equivalent

Hex | Decimal Equivalent |

9AC3 | 39,619 |

Hex = Decimal | Hex
= Dec |
Comment | Hexadecimal number to be converted |
Decimal Equivalent | Dec Equi | |||

0=0 1=1 2=2 4=4 5=5 6=6 7=7 8=8 9=9 A=10 B=11 C=12 D=13 E=14 F=15 |
Columns are numbered from right to left, starting at column zero, not column one | col 3 |
col 2 |
col 1 |
col 0 |
|||

Write the hex number with one digit per column | 9 | A | C | 3 | ||||

Convert the hex digit to decimal | 9 | 10 | 12 | 3 | ||||

Multiply each digit by 16 to the power of n, where n is the column number | 9 x (16^3) | 10 x (16^2) | 12 x (16^1) | 3 x (16^0) | ||||

Put the answer in this row, and add all the answers together | 36,864 | + 2,560 | + 192 | + 3 | = 39,619 |

DEFINITIONS:

16^3 = 16 to the power of 3 = (16 x 16 x 16) = 4,096

16^0 = 16 to the power of 0 = 1 (anything to the power of zero equals one.)

EXPLANATION:

Each hex digit is multiplied by 16^n, where n is its column number, numbering from right to left, starting at column **zero** (not column 1).

Then all the answers are added together. This gives you the decimal equivalent of the hex number you started with.

A GENERAL FORMULA CAN BE DERIVED FOR THOSE FAMILIAR WITH MATHEMATICAL NOTATION

Decimal Equiavalent = Σ (Hn x 16^n) from n = 0 to n

where Σ means "sum", n is the column number, and Hn is the hex digit in the n-th column

### EXAMPLE CONVERSION - HEX TO BINARY

Hex = Hexadecimal, Dec = decimal, Bin = Binary, Bin Equi = Binary Equivalent

Hex | Binary Equivalent |

9AC3 | 1001 1010 1100 0011 |

Hex
= Binary |
Hex
= Bin |
Comment | Hex number to be converted |
Binary Equivalent | Bin Equi | |||

0=0000 1=0001 2=0010 3=0011 4=0100 5=0101 6=0110 7=0111 8=1000 9=1001 A=1010 B=1011 C=1100 D=1101 E=1110 F=1111 |
Hex is directly related to binary and the order of conversion does not matter. You can start at column 3 or column zero. | col 3 |
col 2 |
col 1 |
col 0 |
|||

Write the hex number with one digit per column | 9 | A | C | 3 | ||||

Convert each hex number directly into binary | 1001 | 1010 | 1100 | 0011 | ||||

The usual use of binary is in computers where the binary digits are called bits and are grouped by 8's to make one byte (one byte = 8 bits) | 1001 1010 | 1100 0011 | 1001 1010 1100 0011 | 1001 10101100 0011
These 2 rows of numbers should be written on 1 line |