Converting 16-bit binary to denary

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Quick Questions

Shade in the A or B circle for each question.

1. Which place values do you add together when converting 16-bit binary to denary?

A Every place value, including the 0 columns

B Only the place values that have a 1 under them

2. A 16-bit number has a 1 in the leftmost column only. What is that column worth?

A 32768

B 16384

3. What is 0000000000000101 in denary?

A 5

B 4

4. What is 0000000100000000 in denary?

A 128

B 256

5. Splitting 00000001 00001010 into two bytes, what is the denary value?

A 266

B 11

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
10000000000000101		ALeading zeros add nothing, so only the 4 and 1 columns count: 4 + 1 = 5
21000000000000001 = 32768 + 1 = 32769		BThe 1 is in the 256 column, not the 128 column. The place values must continue up to 32768, so the answer is 256.
3Split the 16-bit number into two bytes, find the value of each byte's 1s, then add the two totals		COnly the first and last columns have a 1, so you add 32768 and 1 and skip all the 0 columns
4Skip the 0 columns and add only the place values that have a 1 under them		DThe 4 column has a 0 under it, so it should be skipped. The correct sum is 8 + 2 = 10.
50000000000001010 = 8 + 4 + 2 = 14		E00000001 00000011 = 256 + 3 = 259
60000000100000000 = 128		F0100000000100000 = 16384 + 32 = 16416

Definitions

add the place values with a 1

Fill in the Blanks

Complete each line of code by filling in the missing parts.

32768 16384 ____ 4096 2048 1024 512 256

0000000000000101 = _ + 1 = 5

0000000100000000 = ___

High byte 00000001 = 1 x 256 Low byte 00000011 = 2 + 1 Total = 256 + _ = 259

1000000000000001 = 32768 + _ = 32769

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A Binary: 0000 0000 1010 0101

B Leading zeros add nothing

C Add: 128 + 64 + 4 + 1

D Denary: 165

Question 2

A Binary: 0000000100000001

B Ones at: 128 and 1

C 256 + 1 = 257

Question 3

A Top byte: 00000011

B Top byte = 128 + 64 = 192

C Bottom: 00001010 = 8 + 2 = 10

D 768 + 10 = 778

Question 4

A Binary: 0000000010000001

B Add only the columns with a 0

C 128 + 1 = 129

Question 5

A Binary: 0000000000000111

B Ones: 8, 4, 2, 1

C 8 + 4 + 2 + 1 = 15

Answer Key

Converting 16-bit binary to denary

Section A: Quick Questions

B — Only the place values that have a 1 under them

A — 32768

A — 5

B — 256

A — 266

Section B: Match the Pairs

0000000000000101 → Leading zeros add nothing, so only the 4 and 1 columns count: 4 + 1 = 5

1000000000000001 = 32768 + 1 = 32769 → Only the first and last columns have a 1, so you add 32768 and 1 and skip all the 0 columns

Split the 16-bit number into two bytes, find the value of each byte's 1s, then add the two totals → 00000001 00000011 = 256 + 3 = 259

Skip the 0 columns and add only the place values that have a 1 under them → 0100000000100000 = 16384 + 32 = 16416

0000000000001010 = 8 + 4 + 2 = 14 → The 4 column has a 0 under it, so it should be skipped. The correct sum is 8 + 2 = 10.

0000000100000000 = 128 → The 1 is in the 256 column, not the 128 column. The place values must continue up to 32768, so the answer is 256.

Section C: Definitions

add the place values with a 1 — To convert 16-bit binary to denary, write the place values (32768 down to 1) over the bits, skip the 0 columns, then add the values that have a 1 under them. Leading zeros add nothing.

Section D: Fill in the Blanks

32768 16384 8192 4096 2048 1024 512 256

0000000000000101 = 4 + 1 = 5

0000000100000000 = 256

High byte 00000001 = 1 x 256
Low byte 00000011 = 2 + 1
Total = 256 + 3 = 259

1000000000000001 = 32768 + 1 = 32769

Section E: Spot the Error

C — In 1010 0101 the 64 column has a 0 under it, so it is skipped. The 1s are under 128, 32, 4 and 1, so the line should be Add: 128 + 32 + 4 + 1.

B — The left 1 is the lowest bit of the top byte, which is worth 256 in 16 bits, not 128. The line should be Ones at: 256 and 1.

B — The top byte uses the place values 32768 down to 256, so its last two bits are worth 512 and 256, not 128 and 64. It should be Top byte = 512 + 256 = 768.

B — We skip the 0 columns and add only the place values that have a 1 under them. The line should say columns with a 1.

A — This binary number only has 1s under 4, 2 and 1, so it does not match the 8 that is added later. The program should start with Binary: 0000000000001111.