Y9-Cs. Unit 1: Bases

Bit

short for binary digit, this is the smallest unit of data in a computer. A bit can have the value 1 or 0, corresponding to on or off.

Byte

a group of eight bits

Denary

Number system in base 10

Hexadecimal

Number system in base 16 that can be easily converted into binary.

Leading Zeros

zeroes before the first digit of 1 in a binary number used to lengthen out the binary number to make it a specific length, e.g. 8 bits or 16 bits.

Logical Shift

a binary shift, either left or right, where the cleared positions are filled with only 0s.

Nibble

Half of a byte - a group of 4 bits

Overflow

Error that occurs when a number becomes too large to fit into the number of bits allocated

Place Value

the weighting value of each digit in a number.

Binary

Number system in base 2 that computers use to represent data and instructions. data represented by just two values (e.g. high/low, on/off, 1/0).

In the binary number 1010. What is the place value of the:

1. first 1

2. first 0

3. second 1

4. second 0

what does this align with?

8

4

2

1

the powers of 2 starting from 2^0

how to annotate the base of a number

using subscript

To convert binary binary to denary, add the place values where a _____ is present:

1

To convert denary to binary, create a table with the ___________(1) and use the steps below:

1. Find the __________(2) place value that is less than or equal to the ____________(3) number.

2. Subtract the ___________(4) found from the above step from the ____________(5).

3. Then find the largest place value that is less than or equal to ___________(6) Repeat until you have _______(7) left.

4. Complete the process by adding 0 to all the blanks in the table.

1. binary place values

2. largest

3. denary

4. largest binary place value

5. denary number

6. the result from the above step

7. nothing

a logical shift is where a pattern of (1) is moved (2) or (3) by a (4) of (5).

the empty (5 again) are filled with (6).

bits

left

right

number

places

zeroes

this is an example of… where the zero is coming from the … side

logical shift left

right

this is an example of… where the zero is coming from the … side

logical shift right

left

1. What does each logical shift left of one position do to the denary value of a number?

2. What does each logical shift right of one position do to the denary value of a number?

doubles the number

halves the number

a logical shift left of n multiples the number by… (a number in terms of n)

a logical shift right of n divides the number by… (a number in terms of n)

2ⁿ

2ⁿ

a logical shift left of n (1) the number by 2ⁿ

a logical shift right of n (2) the number by 2ⁿ

multiplies

divides

When a computer does a calculation, it (1) a space in (2) for the result. The size of this space is usually determined in advance. (3) takes place when the result is too (4) for the (5) of bits (6) to hold the (7).

This means (3 - again) is defined as a (7 - again) to an (8) in which a result is (9 - long answer)

reserves

memory

overflow

large

number

reserved

result

operation

too big to display within the allocated number of bits.

Overflow only occurs during (1) or logical shifts to the (2).

When there is overflow to the (3) also known as (4). This is a related issue but rather than overflow is called a (5) where the (6/7) cannot be represented.

multiplication

left

right

division

loss of precision

decimal points

What logical shift of 01101011 would cause an overflow error if 8 bits are reserved for the result?

Why?

LSL2, this is because 2 shifts is needed for some information (a 1) to be lost.

To convert binary numbers into hexadecimal you separate the binary number into a (1) and convert that (2) bit (1 again) into hexadecimal.

The first place value in a hexadecimal number is (3) which can also be shown as (4)

nibbles

4

1

16⁰

List the following hexadecimal letters into denary then binary

A

B

C

D

E

F

10 - 1010

11 - 1011

12 - 1100

13 - 1101

14 - 1110

15 - 1111

Two ways to show a number is in hexadecimal format:

1. putting 0x in front of it

2. a subscript of 16

put these in order from smallest to largest, which one is the largest hexadecimal number that is possible in 2 digits?

0xAB, 0xCA, 0xFF, 0xBE, 0xCD, 0xAA, 0xF9, 0xA1

0xA1

0xAA

0xAB

0xBE

0xCA

0xCD

0xF9

0xFF (largest hexadecimal number possible in 2 digits)