Binary addition works just like the column addition you learned for denary, only the carries come much sooner. Learn the four rules, then find out what happens when the answer is too big for the register.
Add binary numbers in columns from the right, using four rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 0 carry 1, and 1 + 1 + 1 = 1 carry 1. Every register has a predefined limit: an 8-bit register can hold at most 255. If the true result is bigger than the limit, a carry is left over from the leftmost column and an overflow error occurs: the stored answer is wrong.
Fig. 1: 01011011 + 00110110 = 10010001 (91 + 54 = 145), with the carries shown in red
Section 01
The four rules.
In the lab, set two 8-bit numbers and step through the addition one column at a time. Watch where each carry goes.
Column sum
Write
Carry
Why
0 + 0
0
0
nothing to add
0 + 1
1
0
one
1 + 1
0
1
two is 10 in binary
1 + 1 + 1
1
1
three is 11 in binary
Examiner trap
Show your carries. If you only write the answer and it is wrong, you lose every mark; with the carries shown, you can still earn method marks.
Section 02
Adding two bytes.
Line the numbers up, work from right to left, and write each carry above the next column. Check by converting all three numbers to denary.
Worked example No overflow
Add 00101101 and 00011110. Give the answer in 8-bit binary.
Columns 1 and 2 (from the right): 1 + 0 = 1; 0 + 1 = 1.