ECE 275: Digital Design I
Class 82's Complement
1's Complement + 1 Most popular way to represent negative numbers
Example 1
21 => 010101
=> Flip => 101010
=> +1 => 101011
== 2's Complement (-21)
Example 2
110011
== 51 (Unsigned) == -19 (Sign and Mag) == -12 (1's Comp) == -13 (2's Comp)
Example 3
Using 4-bits what is largest and smallest
- Unsigned: 0-15
- Sign & Magnitude: -7-7
- 1's Complement: -7-7
- 2's Complement: -8-7
13 + 10 = Overflow (Can't represent the result given the space allowed)
More addition
3 + 4 = 7
0011
+ 0100
= 0111
5 + -6 = -1
0101
+ 1010
= 1111
-5 + 6 = 1
1011
+ 0110
= 0001
5 + 6 = 11
0101
+ 0110
= 1011
== -5 (another overflow)
-5 + -6 = -11
1011
+ 1010
= 0101
== 5 (subtraction overflow)
-19 + -6 = -25 (Make sure to sign extend) (Lengths of positive numbers must be the same)
101101
+ 111010
= 100111
Binary Codes
ASCII - American Standard Code for Information Interchange
7-bits: 0 to 127 A-Z, a-z, 0-9, Special Symbols (+-%$@#)
8 bits == 1 Byte
Weighted Codes:
BCD (Binary Coded Decimal):
746 == 0111
+ 0100
+ 0110
could be 8-4-2-1
or 6-3-1-1
....
2-out-of-5:
0 - 00011
1 - 00101
2 - 10010
used for error checking
Gray Code:
0 - 0000
1 - 0001
2 - 0011
only a one bit change
used for parity checkers
Excess-3
0 - 0011
1 - 0100
2 - 0101
add 3 to the number
IEEE Floating Point Hardware