文档介绍：Digital concept and Number system
Chapter 1
Binary Codes
group of four binary digits represent a single decimal digit
0 1 2 3 4 5 6 7 8 9
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
Decimal BCD
Natural Binary Coded Decimal (BCD)
0 1 2 3 4 5 6 7 8 9
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
Decimal 8421 2421 Ex-3
0000 0001 0010 0011 0100 1011 1100 1101 1110 1111
0011 0100 0101 0110 0111 1000 1001 1010 1011 1100
Assign fixed weight for each bit position
Weighted Binary Coded Decimal
BCD Self-complementing codes
Self-complementing code is a code whose arithmetic and logic complement are the same.
Logic complements
A logic complement of a binary digit is its opposite value.
The logic complement of 0 is 1 and the logic complement of 1 is 0.
Ex. logic complement of (0011)2 is 1100.
BCD Self-complementing codes
*b is the radix of the numeral x
Two arithmetic complements
Radix complement of x is written x’
X’ = (b) – X
diminish radix complement of x is written x-1’
X-1’ = (b - 1) – X
10s complement (radix complement) of 610
10-6=410
9s complement ( Diminish radix complement ) of 610
10-1-6=310
1
0,
0
1
BCD Self-complementing codes
BCD self-complement are designed so the arithmetic diminished complement can be found by taking the logical complement ,a bit-by-bit inversion of BCD code
0 1 2 3 4 5 6 7 8 9
Decimal 2421 Ex-3
0000 0001 0010 0011 0100 1011 1100 1101 1110 1111
0011 0100 0101 0110 0111 1000 1001 1010 1011 1100
BCD Self-complementing codes
Diminish radix complement
X=610
X-1’ = 10-1-6=310
6ex-3 = 1001
Logic complement of 6ex-3 is 0110.
3ex-3 = 0110
Only one bit change occurs between successive value in this code
Gray code
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Decimal binary Gray
0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110