Page 326 - Embedded Microprocessor Systems Real World Design

Binary: 0001 1101 1110 0110
Hex 1 D E 6

Hex to Decimal
Factor each hex digit by the corresponding power of 16 and sum the results:
Hex: 1DE6=(1~16')+(Dx16~)+(Ex16')+(1~16")
=(1~4096)+(13~256)+(14x16)+(6 x1)
=4096+3328+224+6
= 7654,,,

Decimal to Hex

Divide the number by 16 and write down the remainder. Divide the integer portion of the
previous result by 16 and write down the remainder. Continue this process until the division
results in zero. Write the remainders in reverse order for the hex equivalent of the decimal
number.
7654/16 = 478 with a remainder of 6
478/16 = 29 with a remainder of 14 (1410 =E,,,)
29/16 = 1 with a remainder of 13 = Dlh)
1/16 = 0 with a remainder of 1

Write the remainders, in hex, in reverse order: 1DE6

Math with Binary and Hex Numbers

Binary numbers (and their hex representations) can be added and subtracted just like
decimal numbers. Where most people get into difficulty is in the carry process. When you
add two decimal digits, say 9 and 7, you get 16. However, the process of doing this addition
involves a carry:
9 + 7 = 6 with a carry of 1. The 1 carries into the next, or tens, digit.

Similarly, binary numbers have carry properties:
0 + 0 = 0, no carry
0 + 1 = 1, no carry
1 + 1 = 0, with a carry to the next binary position
So, if we add 9 and 7 in binary, it looks like this:
9 = 10Ol2
+7 = 011l2
We start by adding the least significant digits:
1 + 1 = 0, with a carry into the next digit

Appendix B 307