System Design Flow and Fixed-point Arithmetic - Digital Design of Signal Processing Systems: A Practical Approach - page 109

unsigned by unsigned: {1 0 b0, a}, {1 0 b0, b}
unsigned by signed: {1 0 b0, a}, {b[15], b}
signed by unsigned: {a[15], a}, {1 0 b0, b}
signed by signed: {a[15], a}, {b[15], b}.

Further to this, there are twomain options for multiplications. One optionmultiplies integer numbers
and the second multiplies Q-format numbers. The Q-format multiplication is also called fractional
multiplication. In fractional signed by signed multiplication, the redundant sign bit is dropped,
whereas for integer sign by sign multiplication this bit is kept in the product.
A unified multiplier that takes care of all types of signed and unsigned operands and both integer
and fractional multiplication is given in Figure 3.18. The multiplier appropriately extends the bits of

a

b

b[15]

a[15]

0 0

1 1 1

1

0 1

0 1

16

Signed/

Signed/Unsigned
Op2

16

Unsigned Op1

1

1

17

17

17 x 17
Signed x Signed
Multiplier
32

Unsigned 0

Signed 1

Integer
Fractional 1

0

P

P[31:0] P[30:0],1'b0

Fractional/Integer

0 1

Signed/Unsigned Op1

Signed/Unsigned Op2

32

32h7FFFFFFF

Check
case

corner

0 1

P

Figure 3.18 Unified multiplier for signed by signed, signed by unsigned, unsigned by unsigned and
unsigned by signed multiplication for both fraction and integer modes, it also cater for the corner case