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

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).

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.

01101000 + 00110100 = ________

• 11011100

• 10011100

• 10011100

• 01111100

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.

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.

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.

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.

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

(a)  

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.

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.

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?

(a)  

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.