Logic Gates and Binary For OCR GCSE Computing

Logic Gates and Binary For OCR GCSE Computing Unit 1 - Theory

Logic Gates AND, OR and NOT Symbols and truth tables

Logic Gates • Why logic gates? They are used to manipulate the signals in the processor. • Logic gates are simple circuits which perform Boolean functions. In other words, a circuit which produces an output based on the input. • Both the input and the output must be 1’s and 0’s and therefore these gates are the basis of all logic circuits. • The 1’s and 0’s are actually where a small voltage is a 1 and a very small voltage is a 0

Logic Gates - NOT • The NOT gate is sometimes known as an INVERTER as it will output the opposite or inverse of the input. • We can show this in a truth table. Input Output 0 1 1 0

Logic Gates - AND • The AND gate takes two inputs and gives an output only if both inputs are true. • We can show this in a truth table. This time we have two inputs A and B. Input A Input B Output 0 0 1 1 1

Logic Gates - OR • The OR gate takes two inputs and gives an output if either one input or the other input or both inputs are true. • We can show this in a truth table. Again we have two inputs A and B. Input A Input B Output 0 0 1 1 1 0 1 1

Combining Logic Gates - NOT & AND NAND • We can also combine two or more gates and create a composite truth table. Input A Input B 0 0 0 1 1 A AND B NOT (A AND B)

Combining Logic Gates - NOT & OR NOR • We can also combine two or more gates and create a composite truth table. Input A Input B 0 0 0 1 1 A OR B NOT (A OR B)

Logic Gates - Worksheet • Complete the logic gates worksheet. • You can use http: //www. neuroproductions. be/logic-lab/ to test your predictions.

Binary Counting in binary - binary to denary. Binary addition.

Binary and Denary • Binary is a number system written in Base 2. • Denary is a number system written in Base 10 - this is the decimal system we use in everyday life. • Later we will also meet Hexadecimal - which is in Base 16. • Lets compare counting in denary to counting in binary. . .

Complete the binary / denary conversions worksheet

We can also perform addition in Binary 1000 +0101 _______

We can also perform addition in Binary 1001 +0101 _______ Don't forget the carry bits!

In exams you often get asked to add two eight bit numbers 01100111 +01010100 _______ Don't forget the carry bits!

In exams you often get asked to add two eight bit numbers - and explain this error. . . 10110101 +0101 We call this _______ an overflow error. What has happened here?

Now complete the binary addition worksheet