How many flip flops are needed to store a number?

Answer 1

It depends on how many bits you need to store the number. You would need one flip flop per binary digit that it takes to represent the number. for example, 4 flip flops could display numbers from 0 to 15, to reach 16, you would need another flip flop. and that would give you the capability to store numbers from 0 to 31. After that the progression of adding additional flip flops goes 32, 64, 128, 256, 512, 1024 ...

Another Answer

"D Flip-Flops" are single bit rudimentary gates that allow the retention of the "D" input during the trigger cycle of the gate. Being a single bit on its own is beneficial for serial communication or downstream clocking. This constitutes bit streams of binary digits (bits) at the supplied clock speed.

Knowing that the D Flip-Flop gate is synonymous with a binary digit in computers, conversation about the gates can be referred to as bits. From this point forward the "D Flip-Flop" will be spoken of as a bit. The power of the bit is derived from groups:

· One (1) grouped bit allows for a single base2 counting unit.

· Two (2) grouped bits allow for a single base4 counting unit.

· Three (3) grouped bits allow for a single base8 (Octal) counting unit.

· Four (4) grouped bits allow for a single base16 (Hexadecimal) counting unit.

· Five (5) represents base32

· Six (6) represents base64

· Seven (7) represents base128

· Eight (8) represents base256

· ...

Since numbering systems have the "Base" number of unique symbols in them, Hexadecimal, or simply Hex, is the preferred "Base" of communication between hardware designers and hardware programmers. This refers to the two Hex numbers (two four bit nibbles) that represent a byte for counting digitally. The sixteen unique symbols used in Hexadecimal are as follows:

"0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F"

Ten of the symbols used in Hex are a copy of all the symbols we use for counting in Decimal, plus the first six capital letters of the English alphabet. Zero is the common symbol for all numbering systems because it represents the common reference… nothing. We always start counting with nothing, and then add to that starting reference. Without Zero, we would not be able to translate from one numbering system to another. A base0 numbering system is undefinable since there are zero symbols to count with. A base1 numbering system would only have one symbol: 0 (zero), which would allow it to count nothing very efficiently. Base2 is the first numbering system that can actually count an infinite number of objects. It uses only two symbols: "0" and "1". Hex groups four bits together and is the first numbering system that efficiently occupies a binary and byte boundary. Hex is the accepted standard for communication about digital logic and its programming. A Binary to Hexadecimal equivalence table follows:

00002 = 016 & 10 & 8 & 4 & 2 & 1

00012 = 116 & 10 & 8 & 4 & 2 <(Binary boundary / 2 symbols / 1 bit group)

00102 = 216 & 10 & 8 & 4

00112 = 316 & 10 & 8 & 4

01002 = 416 & 10 & 8

01012 = 516 & 10 & 8

01102 = 616 & 10 & 8

01112 = 716 & 10 & 8 <(Octal boundary / 8 symbols / 3 bit group)

10002 = 816 & 10

10012 = 916 & 10 <(Decimal boundary / 10 symbols / misaligned bit boundary)

10102 = A16

10112 = B16

11002 = C16

11012 = D16

11102 = E16

11112 = F16 <(Hexadecimal boundary / 16 symbols / 4 bit group)

Since the definition of "Number" is vague in the question, it is hoped that the previous paragraphs will allow us to quantify the reference without requiring a selection. A group of eight (8) bits constitute a byte:

· One byte can be used to count 0 to 25510 (0 to FF16) things before repeating

· Two grouped bytes (16 bits or a Word) can be used to count 0 to 65,53510 (0 to FFFF16) things before repeating

· Two grouped words (32 bits or a Long Word) can be used to count 0 to 4,294,967,29610 (0 to FFFFFFFF16)

As you can see, the power of the bit is in its groups. Pick a "Number" then define the group of bits required to represent it. The following are the decimal equivalents of some of the "Powers of 2":

20 = 1

21 = 210

22 = 410

23 = 810

24 = 1610

25 = 3210

26 = 6410

27 = 12810

28 = 25610

29 = 51210

210 = 102410

211 = 204810

212 = 409610

213 = 819210

214 = 16,38410

215 = 32,76810

216 = 65,53610

232 = 4,294,967,29610

264 = 18,446,744,073,709,551,61610

2128 = 3.4028236692093846346337460743177e+3810

...

Answer 2

2