Number Systems
Gbogbo ọrọ náà
Every photo, song, message and game on a computer is, underneath, nothing but ones and zeros. A computer is built from millions of tiny switches, and a switch has only two states: on or off. Binary is the language those switches speak, and once you can read it you can see how any kind of data is really stored.
In this lesson you will convert fluently between denary, binary and hexadecimal, add binary numbers and spot when they overflow, shift bits to multiply and divide by two, and use two's complement to write negative numbers in binary. These are the most reliable marks in the whole paper because the method is fixed: learn it once and you can never be caught out.
Ebumnobi
- 1 Understand how and why computers use binary to represent all forms of data
- 2 (a) Understand the denary, binary and hexadecimal number systems (b) Convert between (i) positive denary and positive binary (ii) positive denary and positive hexadecimal (iii) positive hexadecimal and positive binary
- 3 Understand how and why hexadecimal is used as a beneficial method of data representation
- 4 (a) Add two positive 8-bit binary integers (b) Understand the concept of overflow and why it occurs in binary addition
- 5 Perform a logical binary shift on a positive 8-bit binary integer and understand the effect this has on the positive binary integer
- 6 Use the two’s complement number system to represent positive and negative 8-bit binary integers
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Number Systems. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- What is the denary value of the binary number 00011010? A. 24 B. 26 C. 28 D. 52 Answer: B
- Which hexadecimal value equals the binary number 11001001? A. C9 B. 9C C. CB D. B9 Answer: A
- A logical shift one place to the right has what effect on a positive binary number? A. multiplies it by 2 B. divides it by 2 C. adds 1 D. inverts the bits Answer: B
- Why do computers use binary to represent data? A. it stores more data than denary B. their switches have only two states C. it is the same as hexadecimal D. humans find it easy to read Answer: B
- An 8-bit register holds 11111111 and 1 is added. The result is: A. stored correctly as 256 B. an overflow error C. shifted left D. converted to hex Answer: B
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Machine-Level Information Representation
"Introduction to Computer Science: Machine-Level Information Representation" by OpenStax, OpenStax, Rice University, licensed under CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/). Source: https://openstax.org/books/introduction-computer-science/pages/5-3-machine-level-information-representation. Access for free at https://openstax.org/books/introduction-computer-science/pages/1-introduction
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Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Number Systems? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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