Download presentation

Presentation is loading. Please wait.

Published byOdalys Eastlick Modified over 2 years ago

1
**Kuliah Rangkaian Digital Kuliah 7: Unit Aritmatika**

Teknik Komputer Universitas Gunadarma

2
**Topic #7 – Arithmetic Units**

Comparator Adders Half-adder & Full-adder Carry-ripple adder & carry-look-ahead adder Overflow detection Subtractor Multiplier

3
**(Equality) Comparators (using XOR)**

1-bit comparator 4-bit comparator

4
**Half adder Adds two 1-bit input to produce a sum and a carry-out**

Does not account for carry-in S = X’·Y + X·Y = XY Cout = X·Y Inputs Outputs Y 1 S X Cout X Y S Cout

5
**Full adder Building block to realize binary arithmetic operations**

1-bit-wide adder with carry-in, produces sum and carry-out Truth table: X Y Cin S Cout

6
**Designing full adder 1 00 01 11 10 Cout S 1 00 01 11 10**

Cin X 1 Y XY 2 3 6 7 4 5 Cout S Cin X 1 Y XY 2 3 6 7 4 5 S = X’·Y’·(Cin) + X·Y’·(Cin)’ + X·Y’·(Cin)’ + X·Y·(Cin) = X Å Y Å (Cin) Cout = XY + X(Cin) + Y(Cin)

7
Resulting circuit

8
**Alternative: full adder using AND-OR**

X’Y’C-in XY’C-in’ Sum S X’YC-in’ XYC-in X’ X Y’ Y C-in C-in’ X X’ Y Y’ C-in C-in’ Full Adder X Y S C-in C-out XY YC-in C-out XC-in X Y C-in

9
**Q: Do we need C4 for a 4-bit 2’s complement addition?**

Ripple adder Speed limited by carry chain 2 per full adder 2n for an n-bit adder Approach: eliminate or reduce carry chain Carry look-ahead: compute Cin directly from external inputs Q: Do we need C4 for a 4-bit 2’s complement addition?

10
**Carry look-ahead adder**

Let Ci+1 = (Xi·Yi)+ (Xi+Yi)· Ci = Gi + Pi · Ci For a 4-bit adder … C1 = G0 + P0·C0 C2 = G1 + P1·C1 = G1 + P1·G0 + P1·P0·C0 C3 = G2 + P2·G1 + P2·P1·G0 + P2·P1·P0·C0 C4 = G3 + P3·G2 + P3·P2·G1 + P3·P2·P1·G0 + P3·P2·P1·P0·C0 where Gi = Xi · Yi Pi = Xi + Yi This is a 3 level circuit including generating the Gs and Ps Rule of thumb: one carry look-ahead circuit every 4-bit

11
**Carry look-ahead circuit**

Gs and Ps are also useful for generating the sums

12
16-bit carry ripple adder

13
16-bit carry look-ahead adder

14
Subtraction Recall our discussion on subtraction for 2’s complement … X – Y = X + Y + 1 Invert all bits of Y and set Cin to 1 Example: 4-bit subtractor using 4-bit adder Add a control circuit in ALU s.t. same circuit can be used for both addition and subtraction 4-bit Adder X3 X2 X1 X0 D3 D2 D1 D0 C-in C-out C4 Y3 Y2 Y1 Y0 C0 = 1 S3 S2 S1 S0

15
Multipliers 8x8 multiplier

16
Full-adder array

17
Faster carry chain

18
**Binary Multiplication**

An n-bit X n-bit multiplier can be realized in combinational circuitry by using an array of n-1 n-bit adders where is adder is shifted by one position. For each adder one input is the multiplied by 0 or 1 (using AND gates) depending on the multiplier bit, the other input is n partial product bits. X3 X2 X1 X0 x Y3 Y2 Y1 Y0 __________________________ X3.Y0 X2.Y0 X1.Y0 X0.Y0 X3.Y1 X2.Y1 X1.Y1 X0.Y1 X3.Y2 X2.Y2 X1.Y2 X0.Y2 X3.Y3 X2.Y3 X1.Y3 X0.Y3 _______________________________________________________________________________________________________________________________________________ P P P P P P P P0

19
4x4 Array Multiplier

Similar presentations

Presentation is loading. Please wait....

OK

Adders.

Adders.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on condition monitoring job Training ppt on time management Ppt on endangered animals of india Ppt on area of parallelograms Ppt on kpo and bpo Ppt on timing diagram of 8085 microprocessor Plant anatomy and physiology ppt on cells Ppt on net etiquettes Ppt on use of body language in communication Ppt on two step equations