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 paMuravanembiri

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)

010, 011, 012, ...

   ...

090, 091, 092, ... 097, 098, 099, (kana 99 asvika nhamba mbiri kumucheto kurudyi dzinovambazve pana 0, nhamba iri pedo kuruboshwe yokwidzwa kuenda pana 1)

100, 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,

0001, (chinzvimbo chiri kumucheto kurudyi chinovamba pana 0, chinotevera kuruboshwe chokwidzwa)

0010, 0011, (zvinzvimbo zviviri kumucheto kurudyi zvinovamba pana 0, chinotevera kuruboshwe chokwidzwa)

0100, 0101, 0110, 0111, (zvinzvimbo zvitatu kumucheto kurudyi chinovamba pana 0, chinotevera kuruboshwe chokwidzwa)

1000, 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 111011₂.

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.