Converting numbers 0 to 31 with five bits

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Converting numbers 0 to 31 with five bits

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. What is 10110 in denary?
A 26 (16 + 8 + 2)
B 22 (16 + 4 + 2)
2. Which five-bit number is 31?
A 11110
B 11111
3. What is the largest whole number that five bits can show?
A 31
B 32
4. Which is 19 written in five bits?
A 10011 (16 + 2 + 1)
B 10101 (16 + 4 + 1)
5. Which list shows the five binary place values from left to right?
A 16, 8, 4, 2, 1
B 10, 8, 6, 4, 2
B

Match the Pairs

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

Left columnRight column
110110 AAll five place values switched on: 16 + 8 + 4 + 2 + 1 = 31, the biggest five-bit number
211111 B100000 has six bits. Five bits only reach 31 (11111), so 32 does not fit in five bits.
3To write 19 in five bits: 19 = 16 + 2 + 1, so use the 16, 2 and 1 columns C01001
4Numbers below 16 need no 16 column, so the first bit is 0. For example, 9 = 8 + 1 D10011
513 in five bits is 11010 EFive bits worth 16 + 4 + 2, which makes the number 22
632 in five bits is 100000 F11010 is 16 + 8 + 2 = 26, not 13. To make 13 use 8 + 4 + 1, so it should be 01101.
C

Definitions

16 8 4 2 1
D

Fill in the Blanks

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

1.
Five place values: 16, _, 4, 2, 1
2.
10110 = 16 + 4 + 2 = __
3.
31 in five bits is _____
4.
19 = 16 + 2 + 1, so 19 is _____
5.
25 - 16 = _ 9 = 8 + 1, so 25 is 11001
E

Spot the Error

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

Question 1
A Convert 19 to five bits
B 19 - 16 = 3
C 3 = 2 + 1
D 19 is 10101
Question 2
A Place values: 32 16 8 4 2
B Five bits: 5 columns
C Smallest number: 00000 = 0
D Largest number: 11111 = 31
Question 3
A Convert 25 to five bits
B 25 - 16 = 8, 8 - 8 = 1
C Columns: 16 and 8 and 1
D 25 is 11001
Question 4
A Convert 12 to five bits
B 16 is too big, so put 0
C 8 fits: 12 - 8 = 5
D 4 fits, so 12 is 01100
Question 5
A Binary to decimal: 01101
B 16 8 4 2 1
C 0 1 1 0 1
D 8 + 4 + 2 = 14

Answer Key

Converting numbers 0 to 31 with five bits
Section A: Quick Questions
Q1
B — 22 (16 + 4 + 2)
Q2
B — 11111
Q3
A — 31
Q4
A — 10011 (16 + 2 + 1)
Q5
A — 16, 8, 4, 2, 1
Section B: Match the Pairs
Q1
10110 → Five bits worth 16 + 4 + 2, which makes the number 22
Q2
11111 → All five place values switched on: 16 + 8 + 4 + 2 + 1 = 31, the biggest five-bit number
Q3
To write 19 in five bits: 19 = 16 + 2 + 1, so use the 16, 2 and 1 columns → 10011
Q4
Numbers below 16 need no 16 column, so the first bit is 0. For example, 9 = 8 + 1 → 01001
Q5
13 in five bits is 11010 → 11010 is 16 + 8 + 2 = 26, not 13. To make 13 use 8 + 4 + 1, so it should be 01101.
Q6
32 in five bits is 100000 → 100000 has six bits. Five bits only reach 31 (11111), so 32 does not fit in five bits.
Section C: Definitions
Q1
16 8 4 2 1 — The five binary place values. Use a 1 to count a place value and a 0 to skip it. Together they make any whole number from 0 to 31 as five bits, so 31 is 11111.
Section D: Fill in the Blanks
Q1
Five place values: 16, 8, 4, 2, 1
Q2
10110 = 16 + 4 + 2 = 22
Q3
31 in five bits is 11111
Q4
19 = 16 + 2 + 1, so 19 is 10011
Q5
25 - 16 = 9 9 = 8 + 1, so 25 is 11001
Section E: Spot the Error
Q1
D — 19 = 16 + 2 + 1, so the 16, 2 and 1 columns are 1 and the 8 and 4 columns are 0. That gives 10011. 10101 is 16 + 4 + 1 = 21.
Q2
A — The five place values are 16 8 4 2 1. 32 is the sixth place value and belongs to a six-bit number. The line should read 16 8 4 2 1.
Q3
B — 25 - 16 is 9, not 8. Then 9 - 8 = 1, which leaves the 1 column. The line should be 25 - 16 = 9, 9 - 8 = 1.
Q4
C — 12 - 8 is 4, not 5. The leftover 4 fills the 4 column, giving 01100. The line should be 8 fits: 12 - 8 = 4.
Q5
D — The bits 0 1 1 0 1 have 1s under 8, 4 and 1. The 2 column holds a 0, so it is not added. The line should be 8 + 4 + 1 = 13.