Computer Science - 4CP0 PearsonEdexcel

Binary

Gbogbo ọrọ náà

A computer's processor only ever switches between two electrical states, and everything it stores or calculates has to be built out of those two states. Numbers, letters, photographs and even the instructions of the program itself are all, deep down, patterns of binary digits.

In this lesson you will learn to convert confidently between binary, denary and hexadecimal, add two binary numbers and recognise when the result overflows an 8-bit register, shift a binary pattern left and right, and represent both positive and negative whole numbers using sign-and-magnitude and two's complement.

Ebumnobi

Understand that computers use binary to represent data (numbers, text, sound, graphics) and program instructions
Understand how computers represent and manipulate numbers (unsigned integers, signed integers (sign and magnitude, two's complement))
Be able to convert between binary and denary whole numbers (0-255)
Understand how to perform binary arithmetic (add, shifts (logical and arithmetic)) and understand the concept of overflow
Understand why hexadecimal notation is used and be able to convert between hexadecimal and binary

Akọmọ Ojú-ẹkọ

A computer's circuits are built from switches that are only ever fully on or fully off; there is no reliable middle state to detect at high speed. Binary, the base-2 number system using only the digits 0 and 1, maps perfectly onto this: 1 for on, 0 for off. Every kind of data a computer handles, whole numbers, text, sound, images and even the program instructions themselves, is ultimately stored as a pattern of these binary digits (bits), just interpreted differently depending on what it represents.

Ọ dị na ngwa Green Bridge

Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.

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Ọ dị na Android, Windows, macOS, na Linux

Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Binary. 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 8-bit binary number 00110010? A) 48 B) 50 C) 52 D) 56 Answer: B
How many bits are grouped together to form a single hexadecimal digit? A) 2 B) 3 C) 4 D) 8 Answer: C
An 8-bit unsigned register adds 250 and 10. What happens? A) The result 260 is stored correctly B) Overflow occurs and the stored result is incorrect C) The register automatically becomes 16-bit D) The addition is rejected and nothing is stored Answer: B
Which type of shift copies the sign bit into new positions created by a right shift? A) Logical shift B) Arithmetic shift C) Circular shift D) Hexadecimal shift Answer: B
In two's complement, what does the leftmost bit of an 8-bit number represent? A) A place value of +128 B) A place value of -128 C) Always 0 D) The number of bits used Answer: B