# Jenny's Hobby Farm

## (Previously Webelfin Design)

I (Jenny ) used to be an assembler language programmer back in the days of the dinosaurs, nearly 50 years ago. I have written these pages for anyone who is now trying to learn the hex system of numbers that I used to have to interpret on a regular basis in the old days.

# 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 numberto 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 col3 col2 col1 col0 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 numberto 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. col3 col2 col1 col0 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