Binary numbers

When adding binary numbers, it is important to note that:

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 10

Examples:

Find the sum of the following binary numbers:

(a) 10₂ , 11₂  (b) 11, 11  (c) 10₂ , 01₂  (d) 10₂ , 10₂  (e) 101₂ , 111₂  (f) 111₂, 101₂ and 100₂

Solution:

(a) 102+112=1012    (b) 112+112=1102

(c) 102+012=112    (d) 102+102=1002

(e) 1012+1112=11102    (f) 11121012+1002=1010002

CLASS ACTIVITY  

1. Find the sum of the following binary numbers: 110₂, 101₂
2. Obtain the sum of 111₂, 101₂

Subtraction of Digits Binary Numbers

When subtracting binary numbers:

0 – 0 = 0

1 – 0 = 1

1 – 1 = 0

10 -1 = 1

Examples:

Find the difference of the following binary numbers:  (a) 11₂, 10₂  (b) 111₂, 110₂  (c) 110₂, 100₂  (d) 11011₂, 10011₂

Solutions:

(a) 112–102=012    (b) 1112–1102=0012

(c) 1102–1002=10102    (d) 110112–100112=010002

CLASS ACTIVITY   

1. Obtain the difference between 110110₂, 101101₂
2. Calculate the value of 10011₂, − 1011₂

ASSIGNMENT

Calculate the sum or difference of the following set of binary numbers:

(a) 11011010–11010111    (b) 11010111–01101100

(c) 11011010–11010111    (d) 10001100+10010010

(e) 10010010+10010111    (f) 10010111+11000101

(g) 11100011–11000101    (h) 11100011–01111000

PRACTICE QUESTIONS

1. Calculate the following, do all workings in base two:

(i) 11₂ + 110₂

(ii) 101₂ – 10₂

(iii) 1101₂ + 110₂ – 111₂

(iv) 11011₂ – 1011₂ + 1101₂

2. Convert the binary numbers 11101₂and 10111₂to base 10.

Add the two base 10 numbers.

Add the two binary numbers.

Convert your binary answer to base 10. Compare both answers.

3. Convert the binary numbers 11101₂and 10111₂to base 10.

Subtract the two base 10 numbers.

Subtract the two binary numbers.

Convert your binary answer to base 10. Compare both answers.