Here is an example of 4-bit word size:
DRC numbers for n-bit word ranges from +(2n-1 – 1) to –(2 n-1 – 1)
Note that there are two values for zero (Sign-bit = 1 and Sign-bit=0)
Example of Binary DRC or 1 ’s Complement Numbers for a 4-bit word
Binary SM Number (n=4) Decimal Number
d3 D2 d1 d
0 1 1 1 + 7 = +(2^4 -^1 -1)
0 1 1 0 + 6
0 1 0 1 + 5
0 1 0 0 + 4
0 0 1 1 + 3
0 0 1 0 + 2
0 0 0 1 + 1
0 0 0 0 + 0
1 1 1 1 - 0
1 1 1 0 - 1
1 1 0 1 - 2
1 1 0 0 - 3
1 0 1 1 - 4
1 0 1 0 - 5
1 0 0 1 - 6
1 0 0 0 - 7 = -(2^4 -^1 -1)
Radix Complement (RC) or 2’s complement
Majority of Digital Systems use RC since it simplifies the binary arithmetic operation.
To obtain a negative RC or 2’s complement:
Write a positive number with the MSB set to 0 (positive sign)
Negate (Invert) every bit including sign bit
Add a 1 to the result to obtain the negative number
Note: Taking the 2’s complement of the result will return the original positive number.
Below is an example of 4-bit number of SM to RC:
(+5) 10 = (0 1 0 1 )2DRC
( -5) 10 = (1 0 1 0)2DRC
One Sign Bit
0 +
1 -
3 Magnitude Bit