CS: Binary Numbers and Number Systems Worksheet

Question 1

Write the place values for an 8-bit binary number from left to right.

Accepted Answer

The place values are 128, 64, 32, 16, 8, 4, 2, and 1 from left to right.

Question 2

Convert the binary number 1010 to decimal.

Accepted Answer

The binary number 1010 equals 10 in decimal because 8 + 2 = 10.

Question 3

Convert the binary number 1101 to decimal.

Accepted Answer

The binary number 1101 equals 13 in decimal because 8 + 4 + 1 = 13.

Question 4

Convert the decimal number 6 to a 4-bit binary number.

Accepted Answer

The decimal number 6 is 0110 in 4-bit binary because 4 + 2 = 6.

Question 5

Convert the decimal number 15 to a 4-bit binary number.

Accepted Answer

The decimal number 15 is 1111 in 4-bit binary because 8 + 4 + 2 + 1 = 15.

Question 6

Circle the larger value: 1001 or 0111. Explain your answer.

Accepted Answer

1001 is larger because it equals 9 in decimal, while 0111 equals 7 in decimal.

Question 7

Convert the binary number 10000000 to decimal.

Accepted Answer

The binary number 10000000 equals 128 in decimal because only the 128 place has a 1.

Question 8

Convert the decimal number 25 to an 8-bit binary number.

Accepted Answer

The decimal number 25 is 00011001 in 8-bit binary because 16 + 8 + 1 = 25.

Question 9

Add the binary numbers 0011 and 0101. Give the answer in binary and decimal.

Accepted Answer

0011 + 0101 = 1000 in binary. The decimal value is 8 because 3 + 5 = 8.

Question 10

A computer stores a black-and-white pixel using 1 bit. If 0 means white and 1 means black, write the colors for the bit pattern 10110.

Accepted Answer

The bit pattern 10110 represents black, white, black, black, white.

Question 11

Explain why the binary number 100 is not the same value as the decimal number 100.

Accepted Answer

The binary number 100 uses base 2 place values, so it equals 4 in decimal. The decimal number 100 uses base 10 place values, so it equals one hundred.

Question 12

Convert the decimal number 42 to an 8-bit binary number.

Accepted Answer

The decimal number 42 is 00101010 in 8-bit binary because 32 + 8 + 2 = 42.

CS: Binary Numbers and Number Systems

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