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
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x84. What is the pattern's value N in decimal?

0x84
N =
2.Easy
place values012816403201608040211

Convert the binary number 0100 0001₂ to decimal. Find N.

0100 0001₂
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −119 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −1198 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −5 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −58 bit
U =
5.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 1100 0000 XOR 0011 0100. What is the result's value R in decimal?

1100 0000XOR0011 0100
R =
6.Hard
2680 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 2680 items its own binary code of the same length. What is the smallest number of bits b needed?

2680
b = bit

Answer key

  1. 1. N = 132
  2. 2. N = 65
  3. 3. U = 137
  4. 4. U = 251
  5. 5. R = 244
  6. 6. b = 12 bit

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