IPPJ-The Abstractions in Digital Data Lesson
The Abstractions in Digital Data
When you send a text, read an email, listen to music on your phone, or read the newspaper online, you are using digital data. There are many abstractions in digital data before it gets to the form we recognize and can use. It all starts out as Binary Code.
Data first starts at the lowest level as a binary sequence of 1s and 0s which to a computer equates to a high voltage, or an on state, and a low voltage, or an off state. An electronic device represents the state of anything as being ON or OFF. We flick the switch on the wall and the lights turn on, flick it again, and they turn off. Computer engineers have designed hardware inside the computer that carries out the processes that determine whether a switch is on or off. The hardware is called a logic gate. It is made up of a number of transistor switches arranged in certain ways to produce an on and off signal. Depending on the type of logic gate and whether the input is a 1 or a 0 a decision is made that returns one of two values, either true or false. If the circuit is open, it is on which is represented by 1 and will return true. If the circuit is closed, it is off which is represented by 0 and will return false. The data goes through the logic gates and the CPU turns the signals into a binary code of 8 bits. The CPU, or central processing unit, is the hardware within a computer that carries out the instructions of a computer program by performing the basic arithmetical, logical, control, and input/output operations of the system using binary code.
Binary Number System Presentation
Learn more about the Binary Number System by clicking through the presentation below.
Converting from Binary to Decimal
The chart below shows the base 2 number system for an 8 bit binary code. Working from the right side of a number to the left, the place value of the right most digit is 20, the next place to the left would be the 21 and then the 22 and so forth. The value of each exponent is 1, 2, 4, 8, 16, 32, 64, and 128. The binary number 10011000 is placed starting from right to left into the place value chart.
Refer to the table below. You have the place value for the Base 2 numbering system across the top. The next row shows the value for the place. The binary number is entered into the correct place value location in the table starting from the right and going to the left. Since 1 represents an on circuit and 0 is off, we only count the place value where there is a 1.
Binary code 10011000 is 152. You will add the following place values:
1001 10002 is 128 + 16 + 8 = 15210
Binary Code 011001112 is 10310. You will add the following place values.
0110 01112 is 64 + 32 + 4 + 2 + 1 = 10310
The base of the number is represented as a subscript at the end. Remember, base 2 is binary and base 10 is our decimal system.
To convert from decimal to binary select the corresponding values which equal the base 10 decimal number.
For example, to create the binary number that represents 20210, you would select numbers that total 202.
Converting Decimal to Binary
128+64+8+2=20210
So, in binary code, the decimal number 20210 is equivalent to 110010102.
You have seen that there are many abstractions in digital data. The highest form is the visual output we see after it has been processed by the computer. The lowest form of all digital data is the individual binary bit either 0 or 1.
Binary Activity
Complete the learning activity on converting Binary numbers. Click the arrows. If you struggle with this, contact your instructor. There are test questions involving this process.
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