Muravanembiri

Muchidzidzo masvomhu, **muravanembiri** (binary numeral system in English) zvinoreva tsika yokuverenga nokunyora nhamba kuchishandiswa nhamba mbiri sehwaro hwekuverenga nhamba. Apa kunenge kuchishandiswa *0* na *1* chete. Kuverenga nhamba nenzira iyi kunoshandiswa kuma computer. Nokumwe kutaura tsika inoshandiswa pamuravanembiri ingadzi rumbiridzira, kana toshandura kuEnglish zvoreva kuti – ‘’following twos or by way of two’’.

## Kuverenga pa[[Muravanembiri]]

Kuverenga nhamba paMuravanembiri kunoitwa nenzira yakafanana nokuverenga nhamba paMuravanegumi. Tichitanga nevara rokutanga mavara anorongwa nenzira inoenderana nokukwira kwehuwandu. Kana pari paMuravanegumi panoshandiswa nhamba gumi dzinoti *0,1,2,3,4,5,6,7,8,9*; zvino paMuravanembiri panoshandiswa nhamba mbiri dzinoti *0, 1*.

Kana mavara apedza ese pachinzvimbo chokutanga chiri kurudyi, nhamba iri kuruboshwe inobva yakwidzwa, kuverengwa kwovambazve pana *0* pachinzvimbo chokutanga chiri kurudyi.  Somuenzaniso pamuravanegumi kuverenga kunofamba sezvinotevera:

:000, 001, 002, ... 007, 008, 009, (kana 9 asvika nhamba iri kumucheto kurudyi inovambazve pana 0, nhamba iri pedo kuruboshwe yokwidzwa kuenda pana 1)
:0**1**0, 011, 012, ...
:&nbsp;&nbsp;&nbsp;...
:090, 091, 092, ... 097, 098, 099, (kana 99 asvika nhamba mbiri kumucheto kurudyi dzinovambazve pana 0, nhamba iri pedo kuruboshwe yokwidzwa kuenda pana 1)
:**1**00, 101, 102, ...

Kana nhamba yasvika 9, danho rinotevera kuti chinzvimbo ichocho chivambe pana *0*, nhamba iri pedo kuruboshwe yokwidzwa kuva *1*. PaMuravanembiri panoverengwa nenzira yakafana asi kuchishandiswa mavara maviri *0* na *1*.  Saka kana chinzvimbo chakana kusvika pana *1*, panova nokuvambazve kuenda pana *0*, uye chinzvimbo chiri kuruboshwe chinokwidza kuenda pana *1* sezvinotevera:

:0000,
:000**1**, (chinzvimbo chiri kumucheto kurudyi chinovamba pana 0, chinotevera kuruboshwe chokwidzwa)
:00**1**0, 0011, (zvinzvimbo zviviri kumucheto kurudyi zvinovamba pana 0, chinotevera kuruboshwe chokwidzwa)
:0**1**00, 0101, 0110, 0111, (zvinzvimbo zvitatu kumucheto kurudyi chinovamba pana 0, chinotevera kuruboshwe chokwidzwa)
:**1**000, 1001, ...

PaMuravanembiri, chinzvimbo choga-choga chinomirira muradanuro wa 2 nepawa rinokwira zvichibva kurudyi kuenda kuruboshwe. Kumucheto kurudyi kuna 20, panotevera kuruboshwe pana 21, kwotevera 22, zvichingodaro. 

## Kushandura Muravanembiri kuva Muravanegumi

Matanho anoitwa kuti nhamba iri kuMuravanembiri ishandurwe kuenda kumuravanembiri ndeaya:

a. Tsamanisa nhamba dziri pamuravanembiri nedanho ra 2 riri panhamba imwe neimwe.

b. Chepiri wedzanisa zvitsama izvi zvawawana pamusoro.

Somuenzaniso ngatishandure 10112 kuenda kuhwaro hwa 10. Vara 2 rakanyorwa pasi pa 1011 rinopangidza hwaro 2. Saka nzira inotevedzwa sekutsanangura kuri pamusoro ndeiyi:

1 x 20 = 1 

1 x 21 = 2 

0 x 22 = 0 

1 x 23 = 8

1 + 2 + 0 + 8 = 11

Naizvozvo tinoti 10112 = 1110.

## Kushandura Muravanegumi kuva Muravanembiri

Ngatitevedzei muenzaniso wekushandura 59 yehwaro 10 kuenda kuhwaro 2.

1. Nyora pasi mapawa a 2, ari pasi pa 59 sezvizvi **1, 2, 4, 8, 16, 32**. Danho rinotevera ndi 64 rakakura kupfuura 59, saka rasiiwa.

2. Gova 59 na 32 anova ndiye pawa ra 2 rakanyanya kukura riri pasi pa 59. Nyora pasi kuti 32 anopinda kangani zvizere muna 59. Tinoona anopinda kamwe **(1)** nemusarirwa 59 - 32 = 27.

3. Tora musarirwa 27 wogova nepawa wa 2 rinotevera rinova 16: 27/16 = **1** sare 11.
 
4. Tora musarirwa 11 wogova nepawa ra 2 rinotevera rinova 8: 11/8 = **1** sare 3.

5. Tora musarirwa 3 wogova nepawa ra 2 rinotevera rinova 4: 3/4 = **0** sare 3.

6. Tora musarirwa 3 wogova nepawa ra 2 rinotevera rinova 2: 3/2 = **1** sare 1.

7. Tora musarirwa 3 wogovanisa nepawa ra 2 rinotevera rinova 1: 1/1 = **1** sare 0.

Saka zvinoreva kuti mhinduro yekushandura 5910 kuenda kumuravanembiri ndi **111011<sub>2</sub>**.

Kuti tibate chokwadi panoda kudzorera nhamba iyi kuMuravanegumbi sezvizvi:

1 x 20 = 1 

1 x 21 = 2 

0 x 22 = 0 

1 x 23 = 8

1 x 24 = 16

1 x 25 = 32

1 + 2 + 0 + 8 + 16 + 32 = 59

Kureva kuti svomhu yashandwa nemazvo.