Microsoft Word - Digital Logic Design v_4_6a

1.7. Signed Binary Number Conventions

 Signed Binary Number Representations (3 methods)

 Signed Magnitude (SM)

 Easiest for people to read (Not used by computers)

 Here is an example of Signed Magnitude number with 4-bit word size

 Binary SM numbers for n-bit word ranges from +(2 n-1 – 1) to -(2n-1 – 1)

Note: there are two values for zero (Sign-bit = 1 and Sign-bit=0)

 Example of complete list of binary SM 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 0 0 0 - 0

1 0 0 1 - 1

1 0 1 0 - 2

1 0 1 1 - 3

1 1 0 0 - 4

1 1 0 1 - 5

1 1 1 0 - 6

1 1 1 1 - 7 = -(2^4 -^1 -1)

 Diminished Radix Complement (DRC) or 1’s complement

Some computer systems use this information because it is easier to convert.

 To obtain a negative DRC or 1’s complement:

 Write a positive number with MSB set to 0 (positive sign)

 Negate (Invert) every bit including sign bit to obtain the negative number.

(+5) 10 = (0 1 0 1 )2SM

( -5) 10 = (1 1 0 1)2SM

One Sign Bit

0  +

1  -

3 Magnitude Bit