Combinational Gates • Introduction • Analysis arrangement • Half Adder/Full Adder • Half Subtractor/Full Subtractor • BCD to Excess-3 converter • Arithmetic Circuit – Adder/Subtractor – Parallel Adder/Cascading Adder – BCD Adder – Magnitud Comparator MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 1

Combinational Gates • MSI Circuit (MSI Component) – Decoder – Encoder – Demultiplexer – Multiplexer • Programmable Logic Device – Read-Only-Memory ROM – Programmable ROM (PROM) MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 2

Combinational Gates - Introduction • There are two categories of logic gates – Combinational – Sequential • Combinational logic – Each output depends solely on the current input MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 3

Combinational Gates - Introduction • Sequential Logic – Each output depends on both current and the previous input. Memory (from feed back loop) contains previous information MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 4

Combinational Gates – Analysis Arrangement • Given combinational logic, can you analyze it’s function?

• Step 2 – Mark it’s input and output – Get the function on each starting gate with the nearest gate to the input follows to the output – Draw TT – Get the function of the circuit – Half Adder MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 5

Combinational Gates – Analysis Arrangement • Design arrangement 1. What is the problem Example: Build a full adder which can add two bit.

2. Determine and mark input and output for the circuit Example: Two input and two output is mark as below: 3. Draw TT MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 6

Combinational Gates – Half Adder • 4.

Design arrangement Get simplest Boolean function. Use K-Map 5.

Draw logic diagram MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 7

Combinational Gates – Full Adder • Half adder only adds two bits • To add two binary number, we nee to add three bits (including carry) • Example: • Full Adder can be produced from half adder MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 8

Combinational Gates – Full Adder • Truth table • Use K-map to get SOP form MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 9

Combinational Gates – Full Adder • Other method, use algebra manipulation MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 10

Combinational Gates – Full Adder • From the formula, • Full Adder is constructed from two Half Adder and OR gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 11

Combinational Gates – Half Subtractor • Half subtractor takes two input bit, let say X, Y to get two-bit answer which represent X-Y • Truth Table Answer either positive or negative Negative answer is represented by borrow (B) from the next MSB bit Output B and D, can also be represented by two’s complement MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 12

Combinational Gates – Half Subtractor • From TT • circuit MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 13

Combinational Gates – Full Subtractor • Subtraction of two binary numbers need three input Full subtractor • Contains borrow input from previous LSB • Example MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 14

Combinational Gates – Full Subtractor • TT • K-map MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 15

Combinational Gates – Full Subtractor • Other method, use algebra manipulation MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 16

Combinational Gates – Full Subtractor • With that formula, we get • Full subtractor is constructed from two half subtractor and OR and NOT gate MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 17

Combinational Gates – Code converter • Code converter – take input code and translate it to similar code • Example: BCD converter to Excess-3 Input: BCD digit Output: Excess-3 digit MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 18

Combinational Gates –Code Converter BCD to Excess-3 Truth table K-Map MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 19

Combinational Gates –Code Converter BCD to Excess-3 MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 20

Combinational Gates – Arithmetic Circuit • Half Adder MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 21

Combinational Gates – Arithmetic Circuit • Full Adder MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 22

Combinational Gates – Arithmetic Circuit • Half Subtractor MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 23

Combinational Gates – Arithmetic Circuit • Full Subtractor MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR 24