What is 4x0.5 to the power 19 as a power of 2?

Answer 1

(4*.5)19 = 219 = 549755813888 (if you are looking to evaluate it)

Let's represent 19 in its binary form.

24 23 22 21 20

19 = 10011 (ignore the first one) = 0011 = S S S2 S2, where S = Square and S2 = square and multiply by 2.

So we have: S S S2 S2

22 = 4

42 = 16

162 = 256*2 = 512

5122 = 262144*2 = 524288

5242882 = 274877906944*2 = 549755813888 (the answer)

5122 = (this is not multiplication) 521222 = 250104 + ...

101*2(1*2) = 40

102*2(5*2) = 2000

103*2(5*1) = 10000

250104+ = 262144

000040

002000

010000

5242882 = 522242228282 = 250416046464+...

101*2(8*8)= 1280

102*2(2*8) = 3200

103*2(2*8) = 32000

103*2(4*8) = 64000

104*2(4*8) = 640000

105*2(4*2) = 1600000

104*2(2*8) = 320000

105*2(2*8) = 3200000

106*2(2*2) = 8000000

107*2(2*4) = 160000000

105*2(5*8) = 8000000

106*2(5*8) = 80000000

107*2(5*2) = 200000000

108*2(5*4) = 4000000000

109*2(5*2) = 20000000000

250416046464+ = 274877906944

000000001280

000000003200

000000032000

000000064000

000000640000

000001600000

000000320000

000003200000

000008000000

000160000000

000008000000

000080000000

000200000000

004000000000

020000000000

Note: It is not so much work. I multiply digits one by one, because I can multiply and double them easily. I do not use so big columns, everything can be done quickly, but I wrote them for you to understand how I work.

Answer 2

4 x 0.5^(19) =

2^2 / 2^(19) =

2^2 X 2^(-19) =

2^(2-19) =

2^(-17)