Tugas 8. Rangkuman Fungsi Kombinasi Logika

 Fungsi Kombinasi Logika

Half-Adder

Simple Binary Addition

0 + 0 = 0         Zero plus zero equals zero

0 + 1 = 1         Zero plus one equals one

1 + 0 = 1         One plus zero equals one

1 + 1 = 1         One plus one equals zero with a carry of one

Basic Adder 

Adder are important in computers and also in other types of digital systems in which numerical data are processed The half-adder accepts two binary digits on its inputs and produces two binary digits on its outputs, a sum bit and a carry bit.

Half-Adder Logic

The Full-Adder

 The Full-Adder accepts two input bits and an input carry and generates a sum output and an output carry The basic different between a full-adder and a half-adder is that the full-adder accepts an input carry.

The full-adder must add the two input bits and the input carry. From the half-adder, the sum of the input bits A and B is the exclusive-OR of those two variables. For the input carry (Cin) to be added to the input bits, it must be exclusive-ORed, and last yield the equation for the sum output of the full-adder

This is mean that to implement the full-adder sum function, two 2-input exclusive-OR gates can be used . The first must generate the term AB and the second has as its inputs the output of the first XOR gate and the input carry. The output carry is a 1 when both inputs to the first XOR gate are 1s or when both inputs to the second XOR gate are 1s. The output carry of full-adder is therefore produced by the inputs A ANDed with B and AB ANDed with Cin.

Full Adder from Two Half-Adder Circuits

Example: Determine the outputs for the inputs shown

Parallel Binary Adder 

A single full-adder is capable of adding two 1-bit numbers and an input carry. To add binary numbers with more than one bit, we must use additional full-adders.

Example: Determine the sum generated by the 3-bit parallel adder

Four-Bit Parallel Adders 

4-Bits – Nibble

Truth Table for a 4-Bit Parallel Adder

Use the 4-bit parallel adder truth table to find the sum and output carry for the following two 4-bit numbers if the input carry (Cn-1) is 0. A4A3A2A1 = 1100, B4B3B2B1 = 1100

Example: Show how two 74LS283 adders can be connected to form an 8-bit parallel adder. Show output bits for the following 8-bit input numbers: A8A7A6A5A4A3A2A1 = 10111001 and B8B7B6B5B4B3B2B1 = 10011110

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