Number systems worksheet with answers

Free printable Number systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
place values112806403211608041201

Convert the binary number 1001 0010₂ to decimal. Find N.

1001 0010₂
N =
2.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x9A. What is the pattern's value N in decimal?

0x9A
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −119 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −1198 bit
U =
4.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −17 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −178 bit
U =
5.Hard
1269 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1269 items its own binary code of the same length. What is the smallest number of bits b needed?

1269
b = bit
6.Hard
4531 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 4531 items its own binary code of the same length. What is the smallest number of bits b needed?

4531
b = bit

Answer key

  1. 1. N = 146
  2. 2. N = 154
  3. 3. U = 137
  4. 4. U = 239
  5. 5. b = 11 bit
  6. 6. b = 13 bit

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