Microsoft Word - Digital Logic Design v_4_6a

 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