Binary System Exercise

Write the following numbers in the Binary System:

a) 5

b) 23

c) 88

Answers: Set up the powers of 2 as follows, with units (2⁰) on the right.

2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰

64 32 16 8 4 2 1

a) 1 0 1 = 5

1*4 + 1*1 = 5

Thus, 5 is written as 101.

b) 1 0 1 1 1

1*16 + 1*4 +1*2 +1*1 = 23

c) 1 0 1 1 0 0 0 = 88

Binary Addition Rules:

0+0=0 1+1=0, with a carry over of 1 to the next place.

0+1=1 1+1+1 = 1, with a carry over of 1 to the next place

1+0=1

Add the following:

1011 1100 101 11101

+111 +101 +101 +1100

_____ _____ _____ ______

Convert to binary and add:

a) 39 + 21 b) 123 + 100