IGCSE CS: Ch.1 Number bases (CIE 0478, 23-25)

1.

Multiple Choice

30 sec

4 pts

Computers store and transmit information using _________ digits.

Denary

Binary

Octal

Hexadecimal

Answer explanation

Computers use binary digits—zeroes and ones—to store and transmit information in electrical form. Each of these binary digits, or "bits", can either be ON (1) or OFF (0).

2.

Multiple Choice

30 sec

4 pts

Octal numbers use digits from 0 to ________.

8

1

7

F

Answer explanation

Octal numbers use the digits 0, 1, 2, 3, 4, 5, 6, and 7 to represent values in base 8 form.

3.

Multiple Choice

30 sec

4 pts

01101000 + 00110100 = ________

11011100

10011100

01111100

4.

Multiple Choice

30 sec

8 pts

Logically shifting all the digits of a binary number one place to the LEFT is the same as...

Multiplying the number by -1

Multiplying the number by 2

Dividing the number by 2

Dividing the number by 0

Answer explanation

A logical shift one place to the left is the same as doubling the number, that is, multiplying it by 2. A logical shift one place to the right would be the same as halving the number, that is, dividing it by 2.

5.

Multiple Choice

30 sec

4 pts

Convert the following decimal numbers into hexadecimal: 10, 12, 13, 16.

A, C, D, 10

A, C, E, F

A, C, D, F

A, C, E, 10

Answer explanation

Hexadecimal numbers use the letters A, B, C, D, E, and F to represent values of 10, 11, 12, 13, 14, and 15 respectively.

6.

Multiple Choice

30 sec

1 pt

What is the decimal equivalent of the binary number 10110110 (using two's complement form)?

-74

182

-72

150

Answer explanation

In binary 2's complement form, numbers that have "1" in the leftmost place are always negative; those with "0" are always positive.

7.

Multiple Choice

30 sec

4 pts

When you convert HEX E3A7 to binary, what are the first four digits (i.e. the four leftmost digits) of the resulting binary number?

0111

1010

1000

1110

Answer explanation

Each hexadecimal digit corresponds to a group of four binary digits. To find the first four digits of a binary number, simply convert the first digit of the hexadecimal number.

8.

Fill in the Blank

1 min

4 pts

How many sixty-fours are there in the number OCT 731?

Answer explanation

The last digit in an octal number shows how many ones are in the number; the second-last digit shows how many eights are in the number; the third-last, how many sixty-fours; and so on.

9.

Draw

3 mins

8 pts

Draw to add the two binary numbers in this image. Show any carry digits.

Answer explanation

When adding binary digits 1 and 0 together, the sum is 1, and there is no value to carry. When adding binary digits 1 and 1 together, the sum is 0, and a value of 1 is carried to the next column.

10.

Fill in the Blank

1 min

8 pts

Base 3 numbers are also called ternary numbers. The last digit in a ternary number is the "one" place, and the second-last digit is the "three" place. What value does the fifth-last digit represent?

Answer explanation

Reading from right to left, the ternary number 12102 has a value of 2 in the "one" place, 0 in the "three" place, 1 in the "nine" place, 2 in the "twenty-seven" place, and 1 in the "eighty-one" place.

11.

Multiple Choice

30 sec

4 pts

Which of the following is TRUE about binary numbers in two's-complement form?

They can only represent numbers half as large as numbers in normal form

The lowest (rightmost) digit indicates the number's sign (+ve/-ve)

They can only represent half as many negative numbers as positive ones

They must always have eight digits

Answer explanation

As an example, consider 8-bit binary numbers. While you could use them to express numbers from 0 to 255 in normal form, you could only use them to express numbers from 0 to 127 (or -127) in two's-complement form, since the highest (leftmost) bit is used to show the sign. Two's-complement form can be used with any number of bits, as long as the number of bits is constant.

12.

Fill in the Blank

2 mins

4 pts

Mr. Dan sends you the following hexadecimal-encoded message: 46 75 68 6F. What does this message say when decoded using ASCII code (see image)?

13.

Fill in the Blank

1 min

4 pts

A number has six ones, three eights, and two sixty-fours. Write this number in octal form.

14.

Fill in the Blank

1 min

4 pts

A number has a one, no twos, a four, no eights, no sixteens, a thirty-two, and a sixty-four. Write this number in eight-bit binary form.

15.

Fill in the Blank

1 min

5 pts

A number has seven ones, eleven sixteens, three two-hundred-and-fifty-sixes, and twelve four-thousand-and-ninety-sixes. Write this number in hexadecimal form.

16.

Multiple Choice

30 sec

Ungraded

POLL (open answer): How confident do you feel with number bases so far?

100%–90%: I'm pretty good with all of it

89%–70%: There are a few things I don't understand, but it's getting better

69%–55%: I'm a bit lost and need some help

<54%: I'm really struggling with them

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