2.6 Converting from binary to denary and binary addition

Question 1

steps to convert binary to denary

Answer 1

• write out the binary place values
• write down the binary number in the correct position
• multiply the values to give the denary value, and add the answers together to get the total

Question 2

binary addition

Answer 2

• write out the numbers one above the other with an addition sign
• start at the right and add the numbers

1 + 0 = 1
0 + 0 = 0
1 + 1 = 10
1 + 1 + 1 = 11

any extra digits are carried to the next column

Question 3

overflow errors

Answer 3

occur when a calculation produces a result that is greater than the computer can deal with

the results can’t be represented by an 8 bit number as it is over 255

a 9th bit is required for overflow

always mark overflow numbers in answers

Question 4

Convert the binary number 11011001 into a denary number [1]

Answer 4

217

Question 5

Add together the following two 8 bit binary numbers: 00101011 + 00010111 [1]

Answer 5

01000010

Question 6

a) Add together the following two 8 bit binary numbers: 10010111 and 11011000

Express your response in 8 bit binary form [2]

b) identify the problem the addition has created

Answer 6

a) 1 01101111

b) there is an overflow because the result cannot be represented in 8 bits

Question 7

Convert the 8 bit binary number 10010111 into a decimal number [2]

Answer 7

151