Wednesday, 16 May 2018

Binary and Hexadecimal

Hexadecimal (or hex) is a base 16 system used to simplify how binary is represented. A hex digit can be any of the following 16 digits: 0 1 2 3 4 5 6 7 8 9 A B C D E F.
Each hex digit reflects a 4-bit binary sequence.
This table shows each hex digit with the equivalent values in binary and denary.



There are a number of very common needs for a computer, including the need to store and view data.

Computers use electrical signals that are on or off, so they have to see everything as a series of binary numbers. This data is represented as a sequence of 1s and 0s (on and off). All data that we want a computer to process needs to be converted into this binary format.


What is binary?

Binary is a number system that only uses two digits: 1 and 0. All information that is processed by a computer is in the form of a sequence of 1s and 0s. Therefore, all data that we want a computer to process needs to be converted into binary.
The binary system is known as a ‘base 2’ system. This is because:
  • there are only two digits to select from (1 and 0)
  • when using the binary system, data is converted using the power of two.





Examples Of Binary


8 4 2 U

0 1 0 1 = 5

1 1 1 1 = 15

1 0 1 1 = 11

0 0 0 1 = 1









128 64 32 16 8 4 2 U
00000111=7
10000000=128
00001101=14
11111111=255








Boolean

Logic gates 1

There are different types of logic gate, depending upon what the gate is needed to do.

OR gates

An OR gate will give a high output if any of the inputs is high. For example, in a simple lighting circuit with two switches in parallel the lamp will light if either switch is pressed.
The relationship between the inputs and the output can be captured in a truth table. A and B represent the inputs and Q is the output.

Truth table for an OR gate

ABQ
000
011
101
111
Circuit symbol of OR gate
OR gate symbol

AND gates

An AND gate will give a high output only if all of the inputs are high. For example, in a simple lighting circuit with two switches in series the lamp will light only if both switches are pressed.

Truth table for an AND gate

ABQ
000
010
100
111



Introduction

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