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‫Welcome to the BCT display explained lecture in this lecture I'm going to introduce and explain how

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‫binary coded decimal display works.

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‫What is binary code of decimal binary code decimal or also known as BCT.

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‫This represents a spread of bits to a single digit A for obesity value ranges from 0 to 9.

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‫A traditional binary value will range from zero to the highest number possible with the given number

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‫of bits.

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‫The advantage of using BCT is that it's much easier for humans to understand now the downfall of using

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‫a binary code of decimal is that it's not the most efficient use of bits in a register.

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‫So let's take a look at a standard binary counterexample.

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‫We have a binary counter.

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‫That's four bits wide.

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‫We want to count from 0 to 15.

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‫So we are binary value starts out at zero which gives us the for 4 bits.

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‫We have four zeroes in our largest value which are be four ones gives us a hexadecimal value of f and

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‫a decimal value of 15.

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‫And so if we count true we're using every single combination of those four bits.

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‫And there's a total of 16 combinations and we go through all of them counting from 0 to 15 in decimal.

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‫However when our counter is displayed we can display the hexadecimal value which gives us here 1 2 3.

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‫All the way down to F which is which is nice because it's very efficient and we're using every single

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‫bit combination possible.

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‫However it's not the easiest to read or understand if you're seeing multiple digits or you're not an

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‫engineer you know.

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‫So I wouldn't understand how the hexadecimal conversion converts to a decimal value.

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‫So if we take a counter and let's try and do that in binary code a decimal what would that look like.

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‫Well the forbit example would show us we have we start from 0 0 0 0 0 which is the hexadecimal value

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‫of zero and a decimal value of 0 and go to the binary value 0 1 0 0 0 1 which is the hexadecimal value

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‫of 9 and a decimal value of 9.

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‫And if you notice after 1 0 0 1 we have all axes and that just indicates that it's a don't care.

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‫After that our binary code decimal we're not going to display anything.

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‫So we're only displaying hexadecimal and decimal or binary values of 0 2 9 and the disadvantage of this

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‫is we're not using every single combination of the bits available.

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‫So we're not being 100 percent efficient with our memory space

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‫for binary counters are much easier to implement.

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‫However a binary code a decimal counter is much easier to interpret from a human standpoint.

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‫So for example if we have a binary value of 1 0 1 0 0 0 1 0 as far as for humans to read that that becomes

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‫relatively complex or hard to intuitively know what that number is.

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‫So if we take that binary value that is and convert decimal that's 162 and if we convert it to the binary

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‫code a decimal format becomes 0 0 0 1 0 1 1 0 0 0 1 0 which is 1 6 2 or 162 to notice or in binary code

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‫decimal format we're using more bits.

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‫However we're making it easier for humans to read and understand it.

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‫So in our assignment what we do binary binary counters are much easier to implement the binary code

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‫a decimal is a lot easier read.

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‫So we're going to create a counter and then create a design to convert that binary count value into

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‫a binary coded decimal value.

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‫So for our binary to binary code decimal design we are going to use the shift and add 3 algorithm.

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‫So for example if we would have at 8 that binary number we would need to 1 shift the binary number left

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‫one bit and we would need to do this eight times because our number is 8 bits of 8 shifts have taken

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‫place.

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‫The binary code a decimal number is in the hundreds tens and units column of the binary value and any

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‫one of these columns is 5 or greater.

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‫We want to add three to that value in that binary decimal coded column and we'll go back to 1 and just

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‫keep doing this until eight shifts have taken place.

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‫So let's look at an example where instead of 8 we're going to be doing a forbit value.

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‫We're going to convert the hex value d to binary code to decimal.

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‫So first to start out we have the hex in hexadecimal value which in binary is 1 1 1 0.

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‫And when you shift it four times.

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‫However every time we shift we need to check if any number of bits in any one of the columns is greater

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‫than 5 or equal to pi.

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‫We need to add three.

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‫So to start out we'll do our first shift where our units has a value of 1.

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‫So nothing is greater than or equal to five.

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‫We'll shift again or shift number two and once again nothing is greater than or equal to 5.

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‫So you are shift number three.

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‫Now at this point after our shift three in our units column The number is greater than 5.

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‫So we to add three to that units column.

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‫And once we do that our tens call now has a value of 1 in our units column has a value or attends excuse

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‫it has a value 0 or unit has a value of 1 0 1 0.

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‫Now we want to shift for the fourth time.

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‫And when we do this fourth shift we are now in the tens units and we have completed our shift and add

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‫three algorithm which gives us in our tens column of 1 in our units column of 4 which is a value of

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‫14 which is equal to original value of b.

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‫However 14 is much more intuitive and easy to understand for humans as opposed to just saying we or

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‫1 1 1 0.

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‫Now you know how binary code decimal counter works.

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‫Let's go design one.