Decimal to Binary Conversion
Double Dabble (Repeated Division by 2)
1. Divide the decimal value by 2 (the number base)
2. If Remainder = 0
Then write a 0 as LSB (right most digit)
Else write 1 as LSB (right most digit)
3. If Quotient = 0
Then Jump to Step 7
4. Divide Quotient by 2
5. If Remainder = 0
Then write a 0 as the next digit on the left
Else write 1 as the next digit on the left
6. If Quotient ¹ 0
Then Jump to Step 4
7. END (Last remainder is MSB)
Decimal to HEX Conversion
Hex Dabble (Repeated Division by 16)
1. Divide the decimal value by 16 (the number base)
2. If Remainder = 0
Then write a 0 as LSB (right most digit)
Else write the remainder in HEX as LSB (right most digit)
3. If Quotient = 0
Then Jump to Step 7
4. Divide Quotient by 16
5. If Remainder = 0
Then write a 0 as the next digit on the left
Else write the remainder in HEX as the next digit on the left
6. If Quotient ¹ 0
Then Jump to Step 4
7. END (Last remainder is MSB)
BINARY TO DECIMAL CONVERSION
The weighted value for each position is determined as follows (2n):
27 / 26 / 25 / 24 / 23 / 22 / 21 / 20128 / 64 / 32 / 16 / 8 / 4 / 2 / 1
1. Multiply the Binary value for each position and multiply by its weight
2. Add all values
EXAMPLE 0110 1011B ® Decimal
0 * 128 / 01 * 64 / 64
1 * 32 / 32
0 * 16 / 0
1 * 8 / 8
0 * 4 / 4
1 * 2 / 2
1 * 1 / 1
111
HEX TO DECIMAL CONVERSION
The weighted value for each position is determined as follows (16n):
164 / 163 / 162 / 161 / 16065536 / 4096 / 256 / 16 / 1
1. Multiply the Hex value for each position and multiply by its weight
2. Add all values
EXAMPLE
39F1AH ® Decimal
3 * 65,536 / 196,6089 * 4096 / 36,864
15 * 256 / 3,840
1 * 16 / 16
10 * 1 / 10
237,338
BINARY TO HEX CONVERSION
Hexadecimal representation of a Binary number is relatively simple. The largest decimal value that can be represented by a HEX value is 15. (0FH = 15) If we examine a binary number, we notice that the maximum value represented by a nibble (1/2 a byte or 4 bits) and this is also 15D.
23 / 22 / 21 / 208 / 4 / 2 / 1
To Convert a Binary number to HEX
1. Break the binary number into groups on a 4-bit boundary
2. Write the HEX value represented by the 4-bit sequence
Note The weighted positions are only on a nibble boundary or an 8 4 2 1 weight. We are not converting to decimal.
0101 1100 1010 1111B ® H
0101 / 1100 / 1010 / 11115 / C / A / F
Conversion H ® B is the reverse.