Number Systems
Akopọ
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.
Awọn Afojusun
- 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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Oriire fun ipari ẹkọ lori Number Systems. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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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Awọn Iwe Itọsọna Ti a Gba Nimọran
Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
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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