CN102778916A

CN102778916A - Binary measuring implement and binary counting frame

Info

Publication number: CN102778916A
Application number: CN201210147474XA
Authority: CN
Inventors: 胡清六
Original assignee: Individual
Current assignee: Individual
Priority date: 2012-05-05
Filing date: 2012-05-05
Publication date: 2012-11-14

Abstract

'A binary measuring implement and a binary counting frame' show the manner of displaying the existence and the calculation of the quantity by combinations of different binary units, in combination with the manner of displaying the existence and the reading-writing and calculation of the quantity by combinations of different decimal units and the manner of displaying the existence and the reading-writing and calculation of the quantity by combinations of same units in the patent 200610095300.8, the three manners are called three algorithms in mathematics, when a unit value is equal to a position value, a decimal number, a binary number and a natural number are mutually rewritten, and the rewriting shows the change of a quantity formation structure. The decimal number is beneficial to reading and writing the displayed quantity, the binary number is beneficial to calculation of the quantity, and the natural number is beneficial to announcing the increase or decrease of the quantity and the relation of two quantities (simple comparison and ratio). Based on combination of the three algorithms, the mathematics education can be simple, scientific and sustainable, and can keep pace with the times.

Description

Scale-of-two measurer and scale-of-two abacus

Technical field:

The present invention shows a kind of new teaching instrument: with the amount of different binary units making

Tool and abstract calculation tool.

Background technology:

The mankind are the three R'ss that assembly (natural number) with same units goes to show quantity since ancient times: 2006100953008 patents show the three R's that goes to show quantity with the assembly (decimal number) of different decimal units.The present invention is the three R's that the assembly (binary number) with different binary units goes to show quantity.Decimal number, binary number and natural mutual rewriting; Show the change of a quantity composition structure; Decimal number is beneficial to the read-write of quantity, and binary number is beneficial to science and calculates, and natural number is beneficial to the most contacts of measuring and the relation of two quantity of showing; Their integrated application, make that mathematical education is simple, science, sustainable, grow with each passing hour.

Summary of the invention:

The present invention only provides with the assembly of different scale-of-two long measures and shows the measurer of length and abstract calculation tool.

For realizing above-mentioned purpose, the present invention adopts following technology to realize:

The scale-of-two gage: on the rule that shows 1cm (degree of accuracy of base unit, metering), each scale place all shows with 1, from first left " 1 ", below 1, marks respectively: 2 ⁰, 2 ¹, 2 ⁰, 2 ², 2 ⁰, 2 ¹, 2 ⁰, 2 ³, 2 ⁰, 2 ¹, 2 ⁰, 2 ², 2 ⁰, 2 ¹, 2 ⁰, 2 ⁴, 2 ⁰, 2 ¹Show the existence of different scale-of-two long measures.

Scale-of-two is calculated tool: with the abacus of every grade nine pearl in 2006100953008 patents, repack every grade into and go up one on pearl, the abacus that following pearl is four.On the upper beam surface of abacus, mark respectively by gear from left to right: ... 2 ⁵, 2 ⁴, 2 ³, 2 ², 2 ¹, 2 ⁰2 ⁰The sign that shows base unit (least unit in the used unit) shows the literary style of binary number with last pearl by putting the beams in place.

On the central sill of abacus, be denoted as by gear from left to right: ... 10 ⁵, 10 ⁴, 10 ³, 10 ², 10 ¹, 10 ⁰Up and down pearl leans on central sill to show that (annotate: under one on last pearl is at this moment shown five of pearl, pearl and usefulness about in the of every grade can show respectively that 1,2,3,4,5,6,7,8,9 and 0 shows the limited number of this unit to decimal numeral literary style; On abacus middle-grade; Press gear from left to right if mark respectively: ... When ten thousand, thousand, hundred, ten, individual; Pearl and usefulness about in the of every grade; Can show respectively that

numeration mark

1,2,3,4,5,6,7,8,9 has different separately positional value (French famous mathematician Laplce) at diverse location, shows the literary style of nature.Annotate: ten thousand, thousand, hundred, ten, one, be the pronunciation of diverse location value.(... Multifarious a hundred or so is sequence of positions, is not number bit sequence)

Description of drawings:

Fig. 1 is a scale-of-two gage structural representation

Fig. 2 is a decimal system gage structural representation

Fig. 3 is traditional gage (foreign country) structural representation

Fig. 4 is traditional gage (China) structural representation

Fig. 5 is that binary number, decimal number, natural number three are used the abacus structural representation

Embodiment

See Fig. 1, understanding scale-of-two gage, the representation of paying attention to unit promptly: show its meaning with mathematical model (being line segment) here; Show its existence with 1; With its sign (title, symbol, unit value ...) express, the importance of unit sign, both can the amount of showing different classes of; Can show not commensurate big and little of amount of the same race again, here not the sign of commensurate with separately unit value (power) expression.

1, on rule, gesticulate, impression is experienced not commensurate of scale-of-two: 2 ⁰(showing 1cm), 2 ¹(showing 2cm), 2 ²(showing 4cm), 2 ³(showing 8cm), 2 ⁴(showing 16cm)

2, being familiar with the base unit that this chi makes is 1cm, is expressed as 2 on the chi ⁰

3, metering and expression

1. just be certain scale-of-two long measure as if the length that records a thing, as: 2 ⁰=1,2 ¹=2,2 ²=4,2 ³=8,2 ⁴=16

② If an object's length required two or more different combination of display units such as: 2 ¹ +2 ⁰ = 3,2 ² +2 ⁰ = 5,2 ² + 2 ¹ = 6,2 ² +2 ¹ +2 ⁰ = 7,2 ³ +2 ⁰ = 9 ...... Figure 5 number displayed on the beam order of La abacus beads on a stall on the upper beam shows a binary number and calculation

1, understanding number bit sequence ... 2 ⁵2 ⁴2 ³2 ²2 ¹2 ⁰, its shows that adjacent two units in left and right sides relation is the arrangement of 2 the unit of varying in size, 2 ⁰Show base unit (minimum), confirm the position, end of numeral by it.

2, dial pearl and show binary number by putting the beams in place

1. show different long measures: as 2 ⁰ Show 1 in the standard numerical digit, writing (1) ₂2 ₁ Show 1 at left first, write (10) ₂2 ² Second shows 1 on a left side, writing (100) ₂2 ³The 3rd shows 1 on a left side, writing: (1000) ₂

2. show the not length of commensurate's combination: as: 2 ¹+ 2 ⁰2 ¹2 ⁰ Show 11 under two numerical digits, writing (11) ₂2 ²+ 2 ⁰At number bit sequence 2 ²2 ¹2 ⁰Corresponding numerical digit show 1 respectively, the writing (101) ₂2 ²+ 2 ¹, at number bit sequence 2 ²2 ¹2 ⁰Corresponding numerical digit show 1 respectively, the writing (110) ₂2 ²+ 2 ¹+ 2 ⁰Corresponding numerical digit at number bit sequence shows 1 respectively, writing: (111) ₂2 ³+ 2 ⁰, at number bit sequence 2 ³2 ²2 ¹2 ⁰Corresponding numerical digit show 1 respectively, the writing: (1001) ₂

3, calculate and dial pearl

1. addition: identical numerical digit, one or one goes one to advance one on one

2. subtraction: identical numerical digit, one goes one or one to move back one also one.

Claims

1.N ^xUnit of display value, unit shows its meaning with mathematical model, shows that with 1 it exists, with sign (title, symbol, pattern, the unit value of unit ...) express N ^xIn this patent as the sign of unit.N ³N ²N ¹N ⁰, show put in order (number bit sequence) of adjacent two units in left and right sides relation for the unit of varying in size of N (N>=2), with the number of this unit of numerical digit demonstration, form the literary style of N system number, N ⁰Show base unit (minimum), confirm the position, end of numeral by it.N ²N ^-1N ⁰N ^-1N ^-2Show the literary style with N system numerical table registration amount (single-character given name number), N0 shows basic unit place numerical digit (mark decimally), promptly uses N system number, radix point, and what of a quantity are the title of basic unit represent.

2. the said N of claim 1 ^x, its N shows the N system, X shows the position (numerical digit) of a tool unit in big minispread, N ^xUnit of display value.

3. the said N of claim 1 ^x, when it shows a numerical digit, determined the limited maximum (N that are of number of this unit by N ^-1); When N was 2, a numerical digit can only be used the existence of 1 or 0 unit of display together, when N is 10; One numerical digit can only be used the existence of 1,2,3,4,5,6,7,8,9 or 0 unit of display; When N was 16, numerical digit can only use 1,2,3,4,5,6,7,8,9, the existence of a, b, c, d, e, f or 0 unit of display, showed the literary style of 16 systems with Chinese abacus

4 When the unit value and location are equal, to achieve N-ary An interaction with nature An rewritten, rewritten displays a number of changes in the composition and structure.